Pubblicazioni / Publications / Publications

di / of / de

Fabio GAVARINI

  5 Novembre/November/Novembre 2024  

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Lavori in preparazione / Works in progress / Travaux en preparation

• [51]   G. A. García, F. Gavarini, "Multiparameter quantum function algebras and their deformations"


• [50]   S. Chemla, F. Gavarini, N. Kowalzig, "Duality functors for action quantum groupoids"


• [49]   G. A. García, F. Gavarini, "GaGa algebras"

Prepubblicazioni / Preprints / Prepublications

• [48]   G. A. García, F. Gavarini, M. Paolini, "Multiparameter quantum supergroups, deformations and specializations"   -   preprint arXiv:2410.22549 [math.QA]   (2024), 64 pagine/pages/pages
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [47]   G. A. García, F. Gavarini, "Quantum group deformations and quantum R-(co)matrices vs. Quantum Duality Principle", 58 pagine/pages/pages (2024)   -   N.B.: versione estesa in / extended version in / version étendue en arXiv:2403.15096 [math.QA]   (2024), 72 pagine/pages/pages
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [46]   M.-K. Chuah, F. Gavarini, "Super Kähler structures on the complex Abelian Lie supergroups"   -   preprint arXiv:2312.00444 [math.DG]   (2023), 29 pagine/pages/pages
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [45]   M.-K. Chuah, R. Fioresi, F. Gavarini, "Admissible Systems and Graded Hermitian Superspaces"   -   submitted (2020), 15 pagine/pages/pages

Articoli su riviste, Atti, ecc. / Journal articles, Proceedings, etc. / Articles sur journaux, Actes, etc.

• [44]   G. A. García, F. Gavarini, "Formal multiparameter quantum groups, deformations and specializations",   Annales de l'Institut Fourier (in stampa / in press / sous presse), 117 pagine/pages/pages   -   preprint arXiv:2203.11023 [math.QA]   (2022)
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [43]   R. Fioresi, F. Gavarini, "Real forms of complex Lie superalgebras and supergroups",   Communications in Mathematical Physics 397 (2023), no. 2, 937-965   -   DOI: 10.1007/s00220-022-04502-x
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [42]   F. Gavarini, "Quantum duality principle for quantum continuous Kac-Moody algebras",   Journal of Lie Theory 32 (2022), no. 2, 839-862   -   see the journal website
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   PDF & LaTeX: chiedete a / ask to / demandez à gavarini@mat.uniroma2.it


• [41]   G. A. García, F. Gavarini, "Multiparameter quantum groups at roots of unity",   Journal of Noncommutative Geometry 16 (2022), no. 3, 839-926   -   DOI: 10.4171/JNCG/471
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [40]   G. A. García, F. Gavarini, "Twisted deformations vs. cocycle deformations for quantum groups",   Communications in Contemporary Mathematics 23 (2021), no. 8 - 2050084 (56 pages)   -   DOI: 10.1142/S0219199720500844
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [39]   F. Gavarini, "A new equivalence between super Harish-Chandra pairs and Lie supergroups",   Pacific Journal of Mathematics 306 (2020), no. 2, 451-485   -   DOI: 10.2140/pjm.2020.306.451
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [38]   K. Iohara, F. Gavarini, "Singular degenerations of Lie supergroups of type D(2,1;a)",   SIGMA 14 (2018), 137, 36 pages   -   vedasi/see/voir   https://www.emis.de/journals/SIGMA/2018/137/   -   DOI: 10.3842/SIGMA.2018.137
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [37]   S. Chemla, F. Gavarini, N. Kowalzig, "Duality features of left Hopf algebroids",   Algebras and Representation Theory 19 (2016), no. 4, 913-941   -   DOI: 10.1007/s10468-016-9604-9
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [36]   F. Gavarini, "Global splittings and super Harish-Chandra pairs for affine supergroups",   Transactions of the American Mathematical Society 368 (2016), 3973-4026   -   DOI: 10.1090/tran/6456
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [35]   N. Ciccoli, F. Gavarini, "A global quantum duality principle for subgroups and homogeneous spaces",   Documenta Mathematica 19 (2014), 333-380
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [34]   S. Chemla, F. Gavarini, "Duality functors for quantum groupoids",   Journal of Noncommutative Geometry 9 (2015), no. 2, 287-358   -   DOI: 10.4171/JNCG/194
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [33]   F. Gavarini, "Chevalley supergroups of type D(2,1;a)",   Proceedings of the Edinburgh Mathematical Society (2) 57 (2014), no. 2, 465-491   -   DOI: 10.1017/S0013091513000503
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   ,   pdf   -   file TeX / source / fichier TeX


• [32]   R. Fioresi, F. Gavarini, "Algebraic supergroups with Lie superalgebras of classical type",   Journal of Lie Theory 23 (2013), no. 1, 143-158
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [31-Cor]   F. Gavarini, "Corrigendum to Algebraic supergroups of Cartan type",   Forum Mathematicum 28 (2016), no. 5, 1005-1009   -   DOI: 10.1515/forum-2015-0044   -   complemento di / complement to / complement de [31]
•   sunto / abstract / resumé   -   pdf   -   file TeX / source / fichier TeX


• [31]   F. Gavarini, "Algebraic supergroups of Cartan type",   Forum Mathematicum 26 (2014), no. 5, 1473-1564   -   DOI: 10.1515/forum-2011-0144
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX
                vedasi anche il / see also the / voir aussi le Corrigendum!!!


• [30]   R. Fioresi, F. Gavarini, "On the construction of Chevalley supergroups",   in: S. Ferrara, R. Fioresi, V. S. Varadarajan (eds.), Supersymmetry in Mathematics and Physics, UCLA Los Angeles, U.S.A. 2010, Lecture Notes in Mathematics 2027, Springer-Verlag, Berlin-Heidelberg, 2011, pp. 101-123   -   DOI: 10.1007/978-3-642-21744-9_5
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [29]   R. Fioresi, F. Gavarini, "Chevalley supergroups",   Memoirs of the American Mathematical Society 215 (2012), no. 1014, pp. 1-77   -   DOI: 10.1090/S0065-9266-2011-00633-7
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [28]   R. Fioresi, F. Gavarini, "Quantum Duality Principle for Quantum Grassmannians",   in: M. Marcolli, D. Parashar (eds.), Quantum Groups and Noncommutative Spaces. Perspectives on Quantum Geometry, 80-95, Aspects of Mathematics E41, Vieweg+Teubner, Wiesbaden, 2011   -   DOI: 10.1007/978-3-8348-9831-9_4
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [27]   N. Ciccoli, R. Fioresi, F. Gavarini, "Quantization of Projective Homogeneous Spaces and Duality Principle",   Journal of Noncommutative Geometry 2 (2008), no. 4, 449-496   -   DOI: 10.4171/JNCG/26
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [26]   F. Gavarini, "On the radical of Brauer algebras",   Mathematische Zeitschrift 260 (2008), 673-697   -   DOI: 10.1007/s00209-007-0296-z
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [25]   F. Gavarini, "PBW theorems and Frobenius structures for quantum matrices",   Glasgow Mathematical Journal 49 (2007), no. 3, 479-488   -   DOI: 10.1017/S0017089507003813
•   sunto / abstract / resumé   -   pdf   -   file TeX / source / fichier TeX


• [24]   F. Gavarini, Z. Rakic, "F_q[M_n] , F_q[GL_n] and F_q[SL_n] as quantized hyperalgebras",   Journal of Algebra 315 (2007), no. 2, 761-800   -   DOI: 10.1016/j.jalgebra.2007.03.040
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [23]   F. Gavarini, Z. Rakic, "F_q[M₂] , F_q[GL₂] and F_q[SL₂] as quantized hyperalgebras",   Communications in Algebra 37 (2009), no. 1, 95-119   -   DOI: 10.1080/00927870802241238
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [22]   F. Gavarini, "The global quantum duality principle",   Journal für die reine und angewandte Mathematik 612 (2007), 17-33   -   DOI: 10.1515/CRELLE.2007.082
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [21]   N. Ciccoli, F. Gavarini, "Quantum duality principle for coisotropic subgroups and Poisson quotients",   in: N. Bokan, M. Djoric, A. T. Fomenko, Z. Rakic, B. Wegner, J. Wess (eds.), Contemporary Geometry and Related Topics, Proceedings of the Workshop (Belgrade, June 26-July 2, 2005), EMIS ed., 2006, pp. 99-118 - vedasi/see/voir   http://www.emis.de/proceedings/CGRT2005
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [20]   B. Enriquez, F. Gavarini, "A formula for the logarithm of the KZ associator",   SIGMA 2, Vadim Kuznetsov Memorial Issue "Integrable Systems and Related Topics" (2006), Paper 080, 3 pagine/pages/pages   -   DOI: 10.3842/SIGMA.2006.080   -   vedasi/see/voir   http://www.emis.de/journals/SIGMA/2006/Paper080
•   pdf   -   file TeX / source / fichier TeX


• [19]   F. Gavarini, "Presentation by Borel subalgebras and Chevalley generators for quantum enveloping algebras",   Proceedings of the Edinburgh Mathematical Society (2) 49 (2006), no. 2, 291-308   -   DOI: 10.1017/S0013091504000689
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [18]   N. Ciccoli, F. Gavarini, "A quantum duality principle for coisotropic subgroups and Poisson quotients",   Advances in Mathematics 199 (2006), no. 1, 104-135   -   DOI: 10.1016/j.aim.2005.01.009
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [17]   F. Gavarini, "The crystal duality principle: from Hopf algebras to geometrical symmetries",   Journal of Algebra 285 (2005), no. 1, 399-437   -   DOI: 10.1016/j.jalgebra.2004.12.003
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [16]   F. Gavarini, "Poisson geometrical symmetries associated to non-commutative formal diffeomorphisms",   Communications in Mathematical Physics 253 (2005), no. 1, 121-155   -   DOI: 10.1007/s00220-004-1175-7
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [15]   F. Gavarini, "The crystal duality principle: from general symmetries to geometrical symmetries",   in: N. Bokan, M. Djoric, Z. Rakic, A. T. Fomenko, J. Wess (eds.), Contemporary Geometry and Related Topics, Proceedings of the Workshop (Belgrade, 15-21 May 2002), World Scientific, 2004, pp. 223-249
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [14]   B. Enriquez, F. Gavarini, G. Halbout, "Uniqueness of braidings of quasitriangular Lie bialgebras and lifts of classical r-matrices",   International Mathematics Research Notices 46 (2003), 2461-2486   -   DOI: 10.1155/S1073792803208138
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [13]   F. Gavarini, G. Halbout, "Braiding structures on formal Poisson groups and classical solutions of the QYBE",   Journal of Geometry and Physics 46 (2003), no. 3-4, 255-282   -   DOI: 10.1016/S0393-0440(02)00147-X
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [12]   F. Gavarini, "The quantum duality principle",   Annales de l'Institut Fourier 52 (2002), no. 3, 809-834   -   DOI: 10.5802/aif.1902
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   ,   pdf   -   file TeX / source / fichier TeX


• [11]   F. Gavarini, "On the global quantum duality principle",   in: Zoran Kadelburg (ed.), Proceedings of the 10th Congress of Yugoslav Mathematicians (21-24 January 2001; Belgrade, Yugoslavia), Vedes, Belgrade, 2001, pp. 161-168
•   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [10]   F. Gavarini, G. Halbout, "Tressages des groupes de Poisson formels à dual quasitriangulaire",   Journal of Pure and Applied Algebra 161 (2001), no. 2, 295-307   -   DOI: 10.1016/S0022-4049(00)00099-2   -   (hereafter also available in English version)
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [9]   F. Gavarini, "A global version of the quantum duality principle",   Czechoslovak Journal of Physics 51 (2001), no. 12, 1330-1335   -   DOI: 10.1023/A:1013322103870
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [8]   F. Gavarini, "The R-matrix action of untwisted affine quantum groups at roots of 1",   Journal of Pure and Applied Algebra 155 (2001), no. 1, 41-52   -   DOI: 10.1016/S0022-4049(99)00117-6
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [7]   F. Gavarini, "Dual affine quantum groups",   Mathematische Zeitschrift 234 (2000), no. 1, 9-52   -   DOI: 10.1007/s002090050502
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [6]   F. Gavarini, "A PBW basis for Lusztig's form of untwisted affine quantum groups",   Communications in Algebra 27 (1999), no. 2, 903-918   -   DOI: 10.1080/00927879908826468
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [5]   F. Gavarini, "A Brauer algebra theoretic proof of Littlewood's restriction rules",   Journal of Algebra 212 (1999), no. 1, 240-271   -   DOI: 10.1006/jabr.1998.7536
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [4]   F. Gavarini, "Quantum function algebras as quantum enveloping algebras",   Communications in Algebra 26 (1998), no. 6, 1795-1818   -   DOI: 10.1080/00927879808826240
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [3]   F. Gavarini, "Quantization of Poisson groups",   Pacific Journal of Mathematics 186 (1998), no. 2, 217-266   -   DOI: 10.2140/pjm.1998.186.217
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [2]   F. Gavarini, P. Papi, "Representations of the Brauer algebra and Littlewood's restriction rules",   Journal of Algebra 194 (1997), no. 1, 275-298   -   DOI: 10.1006/jabr.1996.7003
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [1]   F. Gavarini, "Geometrical Meaning of R-matrix action for Quantum Groups at Roots of 1",   Communications in Mathematical Physics 184 (1997), no. 1, 95-117   -   DOI: 10.1007/s002200050054
•   sunto / abstract / resumé   -   pdf   -   file TeX / source / fichier TeX


• [0]   F. Gavarini, "Quantizzazione di gruppi di Poisson",   Ph. D. Thesis, Università degli Studi di Roma "La Sapienza" (Roma, ITALY), 1996
•   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX

Saggi non pubblicati / Unpublished Essays / Essais non publiés

• [E3]   F. Gavarini, "Lie supergroups vs. super Harish-Chandra pairs: a new equivalence",   preprint arXiv:1609.02844 [math.RA], 47 pagine/pages/pages   -   vedasi/see/voir   http://arxiv.org/abs/1609.02844   (2016)
•   sunto / abstract / resumé   -   introduzione / introduction / introduction   -   pdf   -   file TeX / source / fichier TeX


• [E2]   F. Gavarini, "The global quantum duality principle: a survey through examples",  in: Proceedings des "Rencontres Mathématiques de Glanon" - 6éme édition (1-5/7/2002; Glanon, France), 2004, 60 pages   -   vedasi/see/voir   http://arxiv.org/abs/1109.3729
•   sunto / abstract / resumé   -   introduction / introduction /introduzione   -   pdf   -   file TeX / source / fichier TeX


• [E1]   F. Gavarini, "The global quantum duality principle: theory, examples, and applications",   120 pages, see   http://arxiv.org/abs/math.QA/0303019   (2003)
•   sunto / abstract / resumé   -   introduction / introduction /introduzione   -   pdf   -   file TeX / source / fichier TeX

Recensioni / Reviews / Critiques

No. 77 reviews di libri e articoli scientifici - tra gli altri, una Featured Review - per Mathematical Reviews (American Mathematical Society ed.), sui seguenti argomenti:
    Teoria degli Invarianti classica e problemi collegati - Algebra lineare e multilineare: teoria delle matrici - Algebre di Lie, bialgebre di Lie, algebre inviluppanti universali e loro rappresentazioni - Categorie monoidali, simmetriche, intrecciate - Gruppi di Coxeter, gruppi di permutazioni, gruppi algebrici, gruppi di Lie, gruppi di Lie-Poisson e loro rappresentazioni - Sistemi hamiltoniani di dimensione finita e infinita, varietà di Poisson di dimensione infinita - Gruppi quantici, gruppi e algebre nelle teorie quantistiche, meccanica quantistica e problema della quantizzazione - Coalgebre, bialgebre, algebre di Hopf e generalizzazioni.