Tokyo Journal of Mathematics

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

Nobuo IIYORI and Masato SAWABE

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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

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

First available in Project Euclid: 28 July 2014

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Zentralblatt MATH identifier

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]


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.

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