%0 Journal Article
%T On the G-invariant Modules
%A Jiarui Fei
%J Mathematics
%D 2014
%I arXiv
%X 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 $kQ\# k[M_G]^*$, 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.
%U http://arxiv.org/abs/1402.6021v1