Crystallizing compact semisimple Lie groups

Abstract: The theory of crystal bases is a means of simplifying the representation theory of semisimple Lie algebras by passing through quantum groups. Varying the parameter q of the quantized enveloping algebras, we pass from the classical theory at ​$q=1$ through the Drinfeld-Jimbo algebras at $q\in]0,1[$ to the crystal limit at $q = 0$. At this point, the main features of the representation theory crystallize into purely combinatorial data described by crystal graphs. In this talk, we will describe what happens to the C*-algebra of functions on a compact semisimple Lie group under the crystallization process, yielding higher-rank graph algebras. This is joint work with Marco Matassa.

category theoryoperator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This online seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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