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arXiv · 1912.01510

On the radical of a Hecke-Kiselman algebra

Jan Okniński·Magdalena Wiertel
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Abstract

The Hecke-Kiselman algebra of a finite oriented graph $\Theta$ over a field $K$ is studied. If $\Theta$ is an oriented cycle, it is shown that the algebra is semiprime and its central localization is a finite direct product of matrix algebras over the field of rational functions $K(x)$. More generally, the radical is described in the case of PI-algebras, and it is shown that it comes from an explicitly described congruence on the underlying Hecke-Kiselman monoid. Moreover, the algebra modulo the radical is again a Hecke-Kiselman algebra and it is a finite module over its center.

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Jan Okniński, Magdalena Wiertel. 2019-12-03. On the radical of a Hecke-Kiselman algebra. https://doi.org/10.1007/s10468-020-09997-3

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