Algebraic monoids and group embeddings

1998/02/16 by A. Rittatore, Rittatore, A. · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/9802073

latex2e, uses epsfig; 21 pages, 1 figure

arxiv created 1998/02/16 · arxiv updated 2009/11/30

Abstract

We study the geometry of algebraic monoids. We prove that the group of invertible elements of an irreducible algebraic monoid is an algebraic group, open in the monoid. Moreover, if this group is reductive, then the monoid is affine. We then give a combinatorial classification of reductive monoids by means of the theory of spherical varieties.

Cited by

• Reductive monoids and cluster algebras
• Root monoids and active algebraic groups

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• Monoid Embeddings of Symmetric Varieties
• On Algebraic Semigroups and Monoids
• Combinatorial characterization of the weight monoids of smooth affine spherical varieties
• Algebraic monoids with affine unit group are affine
• Root monoids and active algebraic groups