On the structure and representations of quantum graph algebras at roots of unity

Stéphane Baseilhac; Matthieu Faitg; Philippe Roche

On the structure and representations of quantum graph algebras at roots of unity

Stéphane Baseilhac, Matthieu Faitg Philippe Roche

13/01/2026

Hopf algebras

quantum groups

invariant theory

representation theory

quan- tized character varieties

AMS subject classification 2020: 17B37, 20G42, 16T20

We study the specializations L ϵ g,n at roots of unity ϵ of odd order of the graph algebras, associated to a simply-connected complex semi-simple algebraic group G and a compact oriented surface Σ • g,n with genus g, n punctures, and one boundary component. We prove that the central localizations of L ϵ g,n , and its subalgebra L uϵ g,n of invariant elements under the coadjoint action of a small quantum group, are central simple algebras of PI degrees that we compute. Also, we describe their centers, and show they are integrally closed rings.

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: On the structure and representations of quantum graph algebras at roots of unity
: Stéphane Baseilhac - Université de Montpellier, IMAG - Institut Montpelliérain Alexander Grothendieck
Matthieu Faitg - Institut de Mathématiques de Toulouse
Philippe Roche - Université de Montpellier, IMAG - Institut Montpelliérain Alexander Grothendieck
: 99231049109311
: IMAG - Institut Montpelliérain Alexander Grothendieck
: English
: Working paper
: hal-05596963