## Séminaire de Géométrie et Quantification |

**Natalia
Iyudu**

(Edinburgh
et IHES)

Sklyanin
algebras via Groebner bases and finiteness conditions for potential
algebras.

Lundi
16 janvier à 15h30, IHP salle **2****01**,

Résumé : I will discuss how
some questions on Sklyanin algebras can be solved using combinatorial
techniques, namely, the theory of Groebner bases, and
elements of homological algebra. We calculate the Poincaré series,
prove Koszulity, PBW, Calabi-Yau, etc., depending on the parameters
of the Sklyanin algebras. There was a gap in the Artin-Schelter
classification of algebras of global dimension 3, where Koszulity and
the Poincaré series for Sklyanin algebras were proved only
generically. It was filled in the Grothendieck Festschrift paper of
Artin, Tate and Van den Bergh, using the geometry of elliptic curves.
Our point is that we recover these results by purely algebraic,
combinatorial means. We use similar methods for generalized Sklyanin
algebras, and for other potential algebras.

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