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Article Dans Une Revue Semigroup Forum Année : 2014

On Algebraic Semigroups and Monoids, II

Michel Brion

Résumé

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.

Dates et versions

hal-01622801 , version 1 (24-10-2017)

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Michel Brion. On Algebraic Semigroups and Monoids, II. Semigroup Forum, 2014, 88 (1), pp.250-272. ⟨10.1007/s00233-013-9528-1⟩. ⟨hal-01622801⟩

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