Constructing Coherently G-invariant Modules

Abstract

Let $G$ be a reductive group acting on a path algebra $kQ$ as automorphisms. We assume that $G$ admits a graded polynomial representation theory, and the action is polynomial. We describe the quiver $Q_G$ of the smash product algebra $kQ\#k[M_G{]}^{\ast }$, where $M_G$ is the associated algebraic monoid of $G$. We use $Q_G$-representations to construct $G$-invariant representations of $Q$. As an application, we construct algebraic semi-invariants on the quiver representation spaces from those $G$-invariant representations.

18 pages, Title changed, Final version to appear J. Algebra (2016)

References in corpus (1)

• Skew group algebras of path algebras and preprojective algebras