Details
| Original language | English |
|---|---|
| Pages (from-to) | 822-859 |
| Number of pages | 38 |
| Journal | Journal of Algebra |
| Volume | 619 |
| Early online date | 30 Dec 2022 |
| Publication status | Published - 1 Apr 2023 |
Abstract
Keywords
- Derived equivalence, Mutation, Periodic algebra, Symmetric algebra, Tame algebra, Weighted surface algebra
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of Algebra, Vol. 619, 01.04.2023, p. 822-859.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Virtual mutations of weighted surface algebras
AU - Holm, Thorsten
AU - Skowroński, Andrzej
AU - Skowyrski, Adam
PY - 2023/4/1
Y1 - 2023/4/1
N2 - The finite-dimensional symmetric algebras over an algebraically closed field, 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 [16]-[20], and it was shown that all these algebras, except few singular cases, are symmetric tame periodic algebras of period \(4\). In this article, using the general form of a weighted surface algebra from [19], 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. We associate such algebras to any triangulated surface, first taking blow-ups of a family of edges to \(2\)-triangle discs, and then virtual mutations of their weighted surface algebras. The results of this paper form an essential step towards a classification of all tame symmetric periodic algebras.
AB - The finite-dimensional symmetric algebras over an algebraically closed field, 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 [16]-[20], and it was shown that all these algebras, except few singular cases, are symmetric tame periodic algebras of period \(4\). In this article, using the general form of a weighted surface algebra from [19], 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. We associate such algebras to any triangulated surface, first taking blow-ups of a family of edges to \(2\)-triangle discs, and then virtual mutations of their weighted surface algebras. The results of this paper form an essential step towards a classification of all tame symmetric periodic algebras.
KW - Derived equivalence
KW - Mutation
KW - Periodic algebra
KW - Symmetric algebra
KW - Tame algebra
KW - Weighted surface algebra
UR - http://www.scopus.com/inward/record.url?scp=85146069378&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2022.11.026
DO - 10.1016/j.jalgebra.2022.11.026
M3 - Article
VL - 619
SP - 822
EP - 859
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -