On the Radical of a Hecke–Kiselman Algebra

Jan Okniński, Magdalena Wiertel
2020 Algebras and Representation Theory  
The Hecke-Kiselman algebra of a finite oriented graph Θ over a field K is studied. If Θ 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
more » ... he radical is again a Hecke-Kiselman algebra and it is a finite module over its center.
doi:10.1007/s10468-020-09997-3 fatcat:lvafff6mtfd2za5jq7eb5gp32m