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- Title
ON THE MORITA REDUCED VERSIONS OF SKEW GROUP ALGEBRAS OF PATH ALGEBRAS.
- Authors
Meur, Patrick Le
- Abstract
Let |$R$| be the skew group algebra of a finite group acting on the path algebra of a quiver. This article develops both theoretical and practical methods to do computations in the Morita-reduced algebra associated to |$R$|. Reiten and Riedtmann proved that there exists an idempotent |$e$| of |$R$| such that the algebra |$eRe$| is both Morita equivalent to |$R$| and isomorphic to the path algebra of some quiver, which was described by Demonet. This article gives explicit formulas for the decomposition of any element of |$eRe$| as a linear combination of paths in the quiver described by Demonet. This is done by expressing appropriate compositions and pairings in a suitable monoidal category, which takes into account the representation theory of the finite group.
- Subjects
REPRESENTATIONS of groups (Algebra); ALGEBRA; FINITE groups; ACCOUNTING
- Publication
Quarterly Journal of Mathematics, 2020, Vol 71, Issue 3, p1009
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmathj/haaa014