Let G be a finite group of Lie type. We construct a finite monoid J? having G as the group of units. JÍ has properties analogous to the canonical compactification of a reductive group. The complex… (More)

Let (W,S) be a finite Weyl group and let w ∈ W . It is widely appreciated that the descent set D(w) = {s ∈ S | l(ws) < l(w)} determines a very large and important chapter in the study of Coxeter… (More)

Let A' be a semisimple algebraic monoid with unit group G. Associated with E is its polyhedral root system (X, 0, C), where X = X(T) is the character group of the maximal torus T c G, $ c X(T) is the… (More)

In this paper we explicitly determine the Renner monoid R and the cross section lattice Λ of the symplectic algebraic monoid MSpn in terms of the Weyl group and the concept of admissible sets; it… (More)

The rook monoid R n is the finite monoid whose elements are the 0 − 1 matrices with at most one nonzero entry in each row and column. The group of invertible elements of R n is isomorphic to the… (More)

In this paper we study the orbit structure of semisimple algebraic monoids with exactly two nonzero minimal G × G-orbits. The case of one minimal orbit was solved earlier by the authors. The key… (More)

Consider the classification problem for irreducible, normal, algebraic monoids with unit group G. We obtain complete results for the groups SI 2 ( AT ) X K*, Gl2(K) and PG12(AT) X K*. If G is one of… (More)

The factorial hull of the projective variety X (or its cone) is a graded algebra R(X) that can be used in some situations to consider simultaneously all divisor classes on X. In this paper we… (More)

Let A" be a nilpotent rational homotopy type such that (1) S(X), the image of the Hurewicz map has finite total rank, and (2) the basepoint map of M, a minimal algebra for X, is an element of the… (More)