Skew group algebras of piecewise hereditary algebras are piecewise hereditary

Details Skew group algebras of piecewise hereditary algebras are piecewise hereditary Skew group algebras of piecewise hereditary algebras are piecewise hereditary

2007-03-17

arxiv.org/abs/math/0703507v3

Mathematics

Rings and Algebras

13 pages, typos corrected. To appear in J. Pure Appl. Algebra

Scientific paper

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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