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# Conjugacy classes and nilpotent variety of a reductive monoid

Published:1998-08-01
Printed: Aug 1998
• Mohan S. Putcha
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## Abstract

We continue in this paper our study of conjugacy classes of a reductive monoid $M$. The main theorems establish a strong connection with the Bruhat-Renner decomposition of $M$. We use our results to decompose the variety $M_{\nil}$ of nilpotent elements of $M$ into irreducible components. We also identify a class of nilpotent elements that we call standard and prove that the number of conjugacy classes of standard nilpotent elements is always finite.
 MSC Classifications: 20G99 - None of the above, but in this section 20M10 - General structure theory 14M99 - None of the above, but in this section 20F55 - Reflection and Coxeter groups [See also 22E40, 51F15]