Monomial 2-Calabi Yau tilted algebras are Jacobian

Abstract: A celebrated result by Keller and Reiten says that 2-Calabi–Yau tilted algebras are Gorenstein and stably 3-Calabi–Yau, in particular Jacobian algebras over an algebraically closed field satisfy this. Jacobian algebras are 2-Calabi-Yau tilted as proven by Amiot. These results originated several conjectures in the opposite direction: Are all 2-Calabi-Yau tilted algebras Jacobian? (Amiot 2011 - Kalck Yang 2020). We show that the converse holds in the monomial case: a 1-Gorenstein monomial algebra that is stably 3-Calabi–Yau has to be 2-Calabi–Yau tilted, moreover it has to be Jacobian. This result can be explained fully in a 50 mins seminar, so I aim to do that.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

( slides | video )

The TRAC Seminar - Théorie de Représentations et ses Applications et Connections