## Tokyo Journal of Mathematics

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

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

Nobuo IIYORI and Masato SAWABE

#### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.3836/tjm/1406552430

**Mathematical Reviews number (MathSciNet)**

MR3264513

**Zentralblatt MATH identifier**

1334.16010

**Subjects**

Primary: 16G20: Representations of quivers and partially ordered sets

Secondary: 20C15: Ordinary representations and characters 20E15: Chains and lattices of subgroups, subnormal subgroups [See also 20F22]

#### 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