On algebraic semigroups and monoids,II |
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Authors: | Michel Brion |
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Affiliation: | 1. Département de Mathématiques, Institut Fourier, UMR 5582, Université de Grenoble I, 38402, Saint-Martin d’Hères Cedex, France
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Abstract: | Consider an algebraic semigroup S and its closed subscheme of idempotents, E(S). When S is commutative, we show that E(S) is finite and reduced; if in addition S is irreducible, then E(S) is contained in a smallest closed irreducible subsemigroup of S, and this subsemigroup is an affine toric variety. It follows that E(S) (viewed as a partially ordered set) is the set of faces of a rational polyhedral convex cone. On the other hand, when S is an irreducible algebraic monoid, we show that E(S) is smooth, and its connected components are conjugacy classes of the unit group. |
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