Skew group algebras of piecewise hereditary algebras are piecewise hereditary

Dionne, Julie; Lanzilotta, Marcelo; Smith, David

Skew group algebras of piecewise hereditary algebras are piecewise hereditary

Authors

Dionne, Julie

Lanzilotta, Marcelo

Smith, David

Description

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