Skew group algebras of deformed preprojective algebras

2010/03/09 by Bo Hou, Hou, Bo, Shilin Yang +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.RT #msc:06B15

paper · pdf · doi:10.48550/arxiv.1003.1797

20 pages

arxiv created 2010/03/21 · arxiv updated 2010/03/23

Abstract

Suppose that Q is a finite quiver and G⊆ \Aut(Q) is a finite group, k is an algebraic closed field whose characteristic does not divide the order of G. For any algebra Λ=kQ/\mathcal I, \mathcal I is an arbitrary ideal of path algebra kQ, we give all the indecomposable ΛG-modules from indecomposable Λ-modules when G is abelian. In particular, we apply this result to the deformed preprojective algebra Π_Q^λ, and get a reflection functor for the module category of Π_Q^λG. Furthermore, we construct a new quiver Q_G and prove that Π_Q^λG is Morita equivalent to Π_Q_G^η for some η.

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