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arXiv · 1810.12612

On the Morita Reduced Versions of Skew Group Algebras of Path Algebras

Patrick Le Meur
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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.

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Patrick Le Meur. 2018-10-30. On the Morita Reduced Versions of Skew Group Algebras of Path Algebras. https://doi.org/10.1093/qmathj%2Fhaaa014

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