Tuesday, April 9, 14:00, 7.527

Panagiotis Kostas (Thessaloniki)
Gorenstein algebras and singularity categories in cleft extensions.

Abstract:
The importance of ring theoretic constructions such as trivial extensions and tensor rings has been established in representation theory of finite dimensional algebras. In this talk, we motivate the study of such constructions via the notion of cleft extension of abelian categories due to Beligiannis. After recalling the basic properties of cleft extensions, we will prove that given two algebras connected by a cleft extension, under natural homological properties, one is Gorenstein if and only if so is the other. We will also prove an analogous result regarding their singularity categories.