PreprintarXiv licencearXiv
Integral quiver presentations for ℛ-trivial semigroup algebras
Abstract
Semigroups in which right divisibility is a partial order, that is, ℛ-trivial semigroups, have been studied by people in algebraic combinatorics in connection with Markov chains (especially left regular bands). Margolis and the author showed that the quiver of the algebra of an ℛ-trivial monoid is field independent. We prove here that the integral semigroup ring of an ℛ-trivial semigroup has a bound quiver presentation provided that it is unital. This then gives a uniform quiver presentation over any field via extension of scalars.
Related
- A criterion for determinantal presentations of numerical semigroup rings
- A quiver presentation of the type D arc algebras and intrinsic formality of 𝔻4
- Derivation based noncommutative geometry of quiver path algebras
- Presentations of skein algebras of genus 2
- Quiver Demazure algebras I: Residue descent, finite quotients, and PBW bases
BibTeX
@misc{steinberg2026integral,
title = {{Integral quiver presentations for $\mathscr R$-trivial semigroup algebras}},
author = {Benjamin Steinberg},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15874},
eprint = {2609.15874},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15874},
}
RIS
TY - UNPB
TI - Integral quiver presentations for ℛ-trivial semigroup algebras
AU - Benjamin Steinberg
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15874
UR - https://arxiv.org/abs/2609.15874
AB - Semigroups in which right divisibility is a partial order, that is, ℛ-trivial semigroups, have been studied by people in algebraic combinatorics in connection with Markov chains (especially left regular bands). Margolis and the author showed that the quiver of the algebra of an ℛ-trivial monoid is field independent. We prove here that the integral semigroup ring of an ℛ-trivial semigroup has a bound quiver presentation provided that it is unital. This then gives a uniform quiver presentation over any field via extension of scalars.
ER -