uu.seUppsala University Publications

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Skew group algebras of Jacobian algebrasPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2019 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 526, p. 112-165Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2019. Vol. 526, p. 112-165
##### National Category

Algebra and Logic
##### Identifiers

URN: urn:nbn:se:uu:diva-355626DOI: 10.1016/j.jalgebra.2019.02.005ISI: 000463309100008OAI: oai:DiVA.org:uu-355626DiVA, id: diva2:1230010
#####

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##### Funder

Swedish Research CouncilAvailable from: 2018-07-02 Created: 2018-07-02 Last updated: 2019-04-25Bibliographically approved
##### In thesis

For a quiver with potential (Q, W) with an action of a finite cyclic group G, we study the skew group algebra Lambda G of the Jacobian algebra Lambda = P(Q, W). By a result of Reiten and Riedtmann, the quiver Q(G) of a basic algebra eta(Lambda G)eta Morita equivalent to Lambda G is known. Under some assumptions on the action of G, we explicitly construct a potential W-G on Q(G) such that eta(Lambda G)eta similar or equal to P(Q(G),W-G). The original quiver with potential can then be recovered by the skew group algebra construction with a natural action of the dual group of G. If Lambda is self-injective, then Lambda G is as well, and we investigate this case. Motivated by Herschend and Iyama's characterisation of 2-representation finite algebras, we study how cuts on (Q, W) behave with respect to our construction.

1. Constructions in higher-dimensional Auslander-Reiten theory$(function(){PrimeFaces.cw("OverlayPanel","overlay1301812",{id:"formSmash:j_idt720:0:j_idt724",widgetVar:"overlay1301812",target:"formSmash:j_idt720:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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