Séminaire de Géométrie et Quantification
(Edinburgh et IHES)
Sklyanin algebras via Groebner bases and finiteness conditions for potential algebras.
Lundi 16 janvier à 15h30, IHP salle 201,
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.