Virtual mutations of weighted surface algebras

The finite-dimensional symmetric algebras over algebraically closed fields, based on surface triangulations, motivated by the theory of cluster algebras, have been extensively investigated and applied. In particular, the weighted surface algebras and their deformations were introduced and studied in...

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Bibliographic Details
Published in:Journal of algebra 2023-04, Vol.619, p.822-859
Main Authors: Holm, Thorsten, Skowroński, Andrzej, Skowyrski, Adam
Format: Article
Language:English
Subjects:
Derived equivalence
Mutation
Periodic algebra
Symmetric algebra
Tame algebra
Weighted surface algebra
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Summary:The finite-dimensional symmetric algebras over algebraically closed fields, based on surface triangulations, motivated by the theory of cluster algebras, have been extensively investigated and applied. In particular, the weighted surface algebras and their deformations were introduced and studied in [14–18], and it was shown that all these algebras, except a few singular cases, are symmetric tame periodic algebras of period 4. In this article, using the general form of a weighted surface algebra from [17], we introduce and study so called virtual mutations of weighted surface algebras, which constitute a new large class of symmetric tame periodic algebras of period 4. We prove that all these algebras are derived equivalent but not isomorphic to weighted surface algebras. The results of this paper form an essential step towards a classification of all tame symmetric periodic algebras.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2022.11.026