Skew group algebras of deformed preprojective algebras
Bo Hou, Shilin Yang

TL;DR
This paper classifies indecomposable modules over skew group algebras of deformed preprojective algebras for abelian groups, introduces a reflection functor, and establishes Morita equivalence with a new quiver algebra.
Contribution
It provides a complete description of indecomposable modules over skew group algebras of deformed preprojective algebras and constructs a Morita equivalence with a new quiver algebra.
Findings
Classification of indecomposable modules for abelian G
Introduction of a reflection functor for module categories
Morita equivalence between skew group algebra and a new quiver algebra
Abstract
Suppose that is a finite quiver and is a finite group, is an algebraic closed field whose characteristic does not divide the order of . For any algebra , is an arbitrary ideal of path algebra , we give all the indecomposable -modules from indecomposable -modules when is abelian. In particular, we apply this result to the deformed preprojective algebra , and get a reflection functor for the module category of . Furthermore, we construct a new quiver and prove that is Morita equivalent to for some .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology
