University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Periodicity for finite-dimensional selfinjective algebras

Periodicity for finite-dimensional selfinjective algebras

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact info@newton.ac.uk.

OASW02 - Subfactors, higher geometry, higher twists and almost Calabi-Yau algebras

 We give a survey on finite-dimensional selfinjective algebras which are periodic as bimodules, with respect to syzygies, and hence are stably Calabi-Yau. These include preprojective algebras of Dynkin types ADE and deformations, as well a class of algebras which we call mesh algebras of generalized Dynkin type. There is also a classification of the selfinjective algebras of polynomial growth which are periodic. Furthermore, we introduce weighted surface algebras, associated to triangulations of compact surfaces, they are tame and symmetric, and have period 4 (they are 3-Calabi-Yau). They generalize Jacobian algebras, and also blocks of finite groups with quaternion defect groups.
 
In general, for such an algebra, all one-sided simple modules are periodic. One would like to know whether the converse holds: Given a finite-dimensional selfinjective algebra A for which all one-sided simple modules are periodic. It is known that then some syzygy of A is isomorphic as a bimodule to some twist of A by an automorphism. It is open whether then A must be periodic.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2017 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity