Osaka Journal of Mathematics

Simplical complexes associated to quivers arising from finite groups

Nobuo Iiyori and Masato Sawabe

Full-text: Open access

Abstract

In this paper, we will introduce a simplicial complex $\mathrm{T}_{Q}(\mathcal{H})$ defined by a quiver $Q$ and a family $\mathcal{H}$ of paths in $Q$. We call $\mathrm{T}_{Q}(\mathcal{H})$ a path complex of $\mathcal{H}$ in $Q$. Let $G$ be a finite group, and denote by $\mathrm{Sgp}(G)$ and $\mathrm{Coset}(G)$ respectively the totality of subgroups of $G$, and that of left cosets $gL \in G/L$ of subgroups $L$ of $G$. We will particularly focus on quivers $Q_{G}$ and $Q_{\mathit{CG}}$ obtained naturally from posets $\mathrm{Sgp}(G)$ and $\mathrm{Coset}(G)$ ordered by the inclusion-relation. Then various properties of path complexes associated to $Q_{G}$ and $Q_{\mathit{CG}}$ will be studied.

Article information

Source
Osaka J. Math., Volume 52, Number 1 (2015), 161-205.

Dates
First available in Project Euclid: 24 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1427202877

Mathematical Reviews number (MathSciNet)
MR3326607

Zentralblatt MATH identifier
1366.20013

Subjects
Primary: 20E15: Chains and lattices of subgroups, subnormal subgroups [See also 20F22]
Secondary: 55U10: Simplicial sets and complexes 06A11: Algebraic aspects of posets

Citation

Iiyori, Nobuo; Sawabe, Masato. Simplical complexes associated to quivers arising from finite groups. Osaka J. Math. 52 (2015), no. 1, 161--205. https://projecteuclid.org/euclid.ojm/1427202877


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