Completely regular algebraic monoids

AbstractBy previous results of Putcha and the author, an irreducible algebraic monoid M is regular if and only if the Zariski closure R(G) ⊆ M is completely regular, where R(G) is the solvable radical of G. Thus, the classification problem leads initially to extreme cases; reductive monoids and completely regular monoids with solvable unit groups.In this paper we classify normal, completely regular (NCR) monoids with solvable unit group. It turns out that each NCR monoid M is determined by its unit group G = TU and the closure Z of T in M. For the converse, we find the exact conditions on a diagram T̄=Z↩T↪G for which there exists an NCR monoid M with Z=T̄⊂M