The lattice of J-classes of (J,sigma)-irreducible monoids

[摘要] In this paper, we introduce a new concept, namely, the (J, sigma)-irreducible monoid. Let G(0) be a simple algebraic group. Let sigma be a surjective endomorphism of G(0) such that (G(0))(sigma) the fixed points of G(0) under sigma, is finite. We construct a (J, sigma)-irreducible monoid M with G the unit group. Extending sigma to M, we obtain a finite monoid M-sigma which is J-irreducible. If M is J-irreducible, we give a precise recipe to determine the lattices of J-classes of M and M-sigma. (C) 1997 Academic Press.

[发布日期] 1997-04-01