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Skew group algebras of piecewise hereditary algebras are piecewise hereditary

Julie Dionne·Marcelo Lanzilotta·David Smith
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Abstract

We show that the main results of Happel-Rickard-Schofield (1988) and Happel-Reiten-Smalo (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and show that if G is a finite group acting on a piecewise hereditary algebra A over an algebraically closed field whose characteristic does not divide the order of G, then the resulting skew group algebra A[G] is also piecewise hereditary.

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Julie Dionne, Marcelo Lanzilotta, David Smith. 2008-05-02. Skew group algebras of piecewise hereditary algebras are piecewise hereditary. https://arxiv.org/abs/math/0703507

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