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| Let ${mathbb F}_q$ be the finite field of $q$ elements and $k$ be its algebraic closure. Let $Q$ be a quiver with automorphism $sigma$. In this survey we focus on the study of modules over the ${mathbb F}_q$-algebra
${frak A}(Q,sigma;q)$ associated with
the pair $(Q,sigma)$ in terms of $F$-stable representations of $Q$ over $k$, and we also discuss several polynomials obtained by
counting numbers of indecomposable
${frak A}(Q,sigma;q)$-modules. In case $Q$ is a tame quiver, we present the formula for the number of isoclasses of indecomposable
${frak A}(Q,sigma;q)$-modules with a fixed dimension vector. |
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| Keywords:quiver with automorphism，hereditary algebra, representation |
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