## Tokyo Journal of Mathematics

### Representations of Path Algebras with Applications to Subgroup Lattices and Group Characters

#### Abstract

Let $Q$ be a quiver, and $w$ a weight function on the set of arrows of $Q$. In this paper, we will introduce an $R$-algebra ${\sf UD}(Q,w;R)$ over a ring $R$ in which the information how vertices of $Q$ are joined by its arrows with weights should be reflected well. This algebra is obtained by using ${\mathbb Z} Q$-modules where ${\mathbb Z} Q$ is the path algebra of $Q$ over ${\mathbb Z}$. We will particularly focus on quivers and weight functions defined by the subgroup lattice of a finite group $G$, and defined by irreducible characters of subgroups of $G$. The structure of the corresponding ${\mathbb Z}$-algebras ${\sf UD}(Q,w;{\mathbb Z})$ and relations with the group $G$ will be studied.

#### Article information

Source
Tokyo J. Math., Volume 37, Number 1 (2014), 37-59.

Dates
First available in Project Euclid: 28 July 2014

https://projecteuclid.org/euclid.tjm/1406552430

Digital Object Identifier
doi:10.3836/tjm/1406552430

Mathematical Reviews number (MathSciNet)
MR3264513

Zentralblatt MATH identifier
1334.16010

#### Citation

IIYORI, Nobuo; SAWABE, Masato. Representations of Path Algebras with Applications to Subgroup Lattices and Group Characters. Tokyo J. Math. 37 (2014), no. 1, 37--59. doi:10.3836/tjm/1406552430. https://projecteuclid.org/euclid.tjm/1406552430

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