Virtual mutations of weighted surface algebras

verfasst von

Thorsten Holm, Andrzej Skowroński, Adam Skowyrski

Abstract

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Nikolaus-Kopernikus-Universität Toruń

Typ

Artikel

Journal

Journal of Algebra

Band

619

Seiten

822-859

Anzahl der Seiten

38

ISSN

0021-8693

Publikationsdatum

01.04.2023

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie

Elektronische Version(en)

http://arxiv.org/abs/2006.13075v2 (Zugang: Offen)
https://doi.org/10.1016/j.jalgebra.2022.11.026 (Zugang: Geschlossen)