Growth rates of indecomposable summands in tensor powers of representations of quivers

TL;DR

This paper studies how the number of indecomposable summands in tensor powers of quiver representations grows, focusing on two common tensor product types.

Contribution

It provides new insights into the growth behavior of indecomposable summands in tensor powers of quiver representations for typical tensor products.

Findings

Analyzes growth rates of indecomposable summands in tensor powers.

Focuses on pointwise and coalgebra-induced tensor products.

Provides theoretical results on growth patterns.

Abstract

Tensor products of quiver representations have been extensively studied; typical examples include the pointwise tensor product and the tensor product induced by the coalgebra structure of path algebras. In this paper, we investigate the growth rates of the number of indecomposable direct summands in tensor powers of quiver representations with respect to these two typical tensor products.