Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771724 | Journal of Algebra | 2017 | 57 Pages |
Abstract
Starting with a highest weight representation of a Kac-Moody group over the complex numbers, we construct a monoid whose unit group is the image of the Kac-Moody group under the representation, multiplied by the nonzero complex numbers. We show that this monoid has similar properties to those of a J-irreducible reductive linear algebraic monoid. In particular, the monoid is unit regular and has a Bruhat decomposition, and the idempotent lattice of the generalized Renner monoid of the Bruhat decomposition is isomorphic to the face lattice of the convex hull of the Weyl group orbit of the highest weight.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Zhenheng Li, Zhuo Li, Claus Mokler,