$\mathscr R$-平凡半群代数的整体箭图表示

中文摘要 AI 辅助

右可除性为偏序的半群，即$\mathscr R$-平凡半群，已被代数组合学领域的研究者结合马尔可夫链（尤其是左正则带）进行研究。Margolis 与作者证明了$\mathscr R$-平凡幺半群代数的箭图与域无关。我们在此证明，$\mathscr R$-平凡半群的整数半群环在其含单位元时具有有界箭图表示。这进而通过标量扩张在任意域上给出统一的箭图表示。

英文摘要

Semigroups in which right divisibility is a partial order, that is, $\mathscr R$-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 $\mathscr R$-trivial monoid is field independent. We prove here that the integral semigroup ring of an $\mathscr R$-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.

发表机构

• City College of New York（纽约市立学院）

机构由 AI 辅助整理，请以论文原文为准。