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      On mutations of selfinjective quivers with potential

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          Abstract

          We study silting mutations (Okuyama-Rickard complexes) for selfinjective algebras given by quivers with potential (QPs). We show that silting mutation is compatible with QP mutation. As an application, we get a family of derived equivalences of Jacobian algebras.

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          Morita Theory for Derived Categories

          Jeremy Rickard (1989)
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            Quivers with potentials and their representations I: Mutations

            Harm Derksen, Jerzy Weyman, Andrei Zelevinsky (2008)
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              Silting mutation in triangulated categories

              Osamu Iyama, Takuma Aihara (2010)
              In representation theory of algebras the notion of `mutation' often plays important roles, and two cases are well known, i.e. `cluster tilting mutation' and `exceptional mutation'. In this paper we focus on `tilting mutation', which has a disadvantage that it is often impossible, i.e. some of summands of a tilting object can not be replaced to get a new tilting object. The aim of this paper is to take away this disadvantage by introducing `silting mutation' for silting objects as a generalization of `tilting mutation'. We shall develope a basic theory of silting mutation. In particular, we introduce a partial order on the set of silting objects and establish the relationship with `silting mutation' by generalizing the theory of Riedtmann-Schofield and Happel-Unger. We show that iterated silting mutation act transitively on the set of silting objects for local, hereditary or canonical algebras. Finally we give a bijection between silting subcategories and certain t-structures.
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                Author and article information

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                Publication date Created: 11 October 2012
                Publication date Updated: 2014-06-13
                Article
                ArXiV ID: 1210.3166
                SO-VID: 9f4cd3a9-dd7b-47d8-ac27-a699acc7022e
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                ACM classes 16G10
                Comments 19 pages, to appear in J. Pure Appl. Algebra
                Categories math.RT math.RA

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