Séminaires : Séminaire d'Algèbre

In 2013, de la Peña initiated the systematic study of algebras of cyclotomic type, that is finite-dimensional algebras of finite global dimension such that some power of their Coxeter matrix is unipotent. For example, fractionally Calabi–Yau algebras have periodic Coxeter matrices. In this talk, we propose a class of algebras, which we call Serre cyclotomic, as a generalization of fractionally Calabi–Yau algebras, and as a categorification of algebras of cyclotomic type. We study dynamical properties of their Nakayama functors and the complexity of their trivial extension algebras. Based on recent work of Chang–Schroll, we characterize Serre cyclotomic gentle algebras. Finally, we provide further examples coming from generalized species. Parts of this ongoing work are joint with Sibylle Schroll.

This talk will take place in hybrid mode at the Institut Henri Poincaré.