Data:	Mercoledì 7 Luglio 2004, Ore 16.30
Luogo:	Aula 1201, Dip. Matematica, U. Roma "Tor Vergata"
Speaker:	Prof. Imre Tuba, Department of Mathematics, Virginia Tech
Titolo:	CLASSIFYING BRAIDED SEMISIMPLE TENSOR CATEGORIES
Abstract:	During much of the last century, symmetries in physical systems were studied via the representation theory of groups and algebras. Up to isomorphism, the classical tensor product of modules over algebras is symmetric under permutation of factors. Recent advances in physics have set the need for more complicated tensor structures, where this symmetry is replaced by noncommutative braiding symmetries, leading to the introduction of braided tensor categories. Of particular interest in conformal field theory are braided tensor categories whose tensor product rules on objects mimic those of finite dimensional representations of quantum groups. I will present some work by David Kazhdan, Hans Wenzl, and myself on classifying braided tensor categories which are thus related to the classical quantum groups (types ABCD). The remarkable result is that something as seemingly innocuous as these tensor product rules largely determines the morphisms and forces these categories to be equivalent to a "twist" of the representation category of the corresponding quantum group. This is proved via a general technique which allows us to "reconstruct" such a category from a related diagonal monoidal algebra, and a careful study of idempotents and traces in Hecke algebras and BMW algebras.