Cohen-Macaulay algebraic monoids

Abstract

Let E E be an irreducible, normal, algebraic monoid with group of units G = G l 2 ( K ) G = {\text {G}}{{\text {l}}_2}(K) , S l 2 ( K ) × K ∗ {\text {S}}{{\text {l}}_2}(K) \times {K^*} or PG l 2 ( K ) × K ∗ {\text {PG}}{{\text {l}}_2}(K) \times {K^*} . Then E E is a Cohen-Macaulay algebraic variety.