Get Algebraic Monoids, Group Embeddings, and Algebraic PDF

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By Mahir Can, Zhenheng Li, Benjamin Steinberg, Qiang Wang

ISBN-10: 1493909371

ISBN-13: 9781493909377

ISBN-10: 149390938X

ISBN-13: 9781493909384

This booklet features a choice of fifteen articles and is devoted to the 60th birthdays of Lex Renner and Mohan Putcha, the pioneers of the sphere of algebraic monoids.

Topics offered include:

structure and illustration conception of reductive algebraic monoids

monoid schemes and purposes of monoids

monoids on the topic of Lie theory

equivariant embeddings of algebraic groups

constructions and homes of monoids from algebraic combinatorics

endomorphism monoids brought on from vector bundles

Hodge–Newton decompositions of reductive monoids

A component to those articles are designed to function a self-contained creation to those themes, whereas the rest contributions are study articles containing formerly unpublished effects, that are guaranteed to develop into very influential for destiny paintings. between those, for instance, the $64000 fresh paintings of Michel Brion and Lex Renner exhibiting that the algebraic semi teams are strongly π-regular.

Graduate scholars in addition to researchers operating within the fields of algebraic (semi)group thought, algebraic combinatorics and the idea of algebraic staff embeddings will take advantage of this special and extensive compilation of a few basic leads to (semi)group idea, algebraic workforce embeddings and algebraic combinatorics merged less than the umbrella of algebraic monoids.

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Additional info for Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics

Example text

Thus, M is quasiprojective as well. t u Another consequence is a version of Chevalley’s structure theorem for an irreducible algebraic monoid; it generalizes [6, Thm. 1], where the monoid is assumed to be normal. Theorem 3. Let M be an irreducible algebraic monoid, G its unit group, and Maff the closure of Gaff in M . (i) Maff is an irreducible affine algebraic monoid with unit group Gaff . (ii) The action of Gaff on Maff extends to an action of G D Gaff Gant , where Gant acts trivially. (iii) The natural map Gant Gant \Gaff Maff !

Thus, the restriction 'jG is the quotient homomorphism . By density, ' is a homomorphism of monoids, and D ı '. So ' is the desired homomorphism. t u Remark 5. M /. M /, are all conjugate in G (Proposition 8). By that proposition, we may take for x any minimal idempotent of M . (ii) As another consequence, any irreducible semigroup S has a universal homomorphism to an algebraic group (in the sense of the above proposition). Indeed, choose an idempotent e in S , and consider a homomorphism of semigroups W S !

2 extend readily to the setting of perfect fields. In view of Theorem 5, every nontrivial algebraic semigroup law on an irreducible curve S is commutative; by Proposition 17 again, it follows that S has an idempotent F -point whenever S and are defined over F . 4 Rigidity In this subsection, we obtain two rigidity results (both possibly known, but for which we could not locate adequate references) and we apply them to the study of endomorphisms of complete varieties. Our first result is a scheme-theoretic version of a classical rigidity lemma for irreducible varieties (see [8, Lem.

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Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics by Mahir Can, Zhenheng Li, Benjamin Steinberg, Qiang Wang

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