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Periodicity for finite-dimensional selfinjective algebras
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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.
This talk is part of the Isaac Newton Institute Seminar Series series.
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