A day on Moduli and Skein algebras in Toulouse

Liste des contributions

1. Structure of moduli algebras and application to skein algebras

Dr Matthieu Faitg

24/03/2023 09:00

The moduli algebra of a compact oriented surface with n punctures (n>0) is a "twisted tensor product" of several copies of the quantized coordinate algebra O_q(G). I will first explain the definition. Then I will present results on the structure of these algebras, namely that they are finitely generated, Noetherian and do not contain zero divisors. If time permits, the ingredients of the...

2. Classification of representations of reduced stated skein algebras

Dr Julien Korinman

24/03/2023 09:45

In this talk, I will introduce a family of algebras named reduced stated skein algebras and present a classification of their finite dimensional (semi-weight) representations.
These representations are conjectured to be the building blocks of some SL_2 TQFT which extend some constructions of Blanchet-Costantino-Geer-Patureau Mirand and Baseilhac-Benedetti.
If time permits, I will explain...

3. On the SL_n stated skein algebra of the triangle

Prof. Thang Le

24/03/2023 10:45

4. Quantum moduli algebras at roots of unity

M. Philippe ROCHE (IMAG)

24/03/2023 11:30

We prove that the graph algebra and the quantum moduli
algebra associated to a punctured sphere and complex semisimple Lie
algebra $\mathfrak{g}$ are Noetherian rings and finitely generated
rings over $\mc(q)$. Moreover, we show that these two properties still
hold on $\mc[q,q^{-1}]$ for the integral version of the graph algebra.
We also study the specializations $\Ll_{0,n}^\e$ of the...