New PDF release: Algebraic Monoids, Group Embeddings, and Algebraic

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

ISBN-10: 1493909371

ISBN-13: 9781493909377

ISBN-10: 149390938X

ISBN-13: 9781493909384

This publication encompasses a selection of fifteen articles and is devoted to the 60th birthdays of Lex Renner and Mohan Putcha, the pioneers of the sector of algebraic monoids.

Topics awarded include:

structure and illustration idea of reductive algebraic monoids

monoid schemes and functions of monoids

monoids regarding Lie theory

equivariant embeddings of algebraic groups

constructions and houses of monoids from algebraic combinatorics

endomorphism monoids caused from vector bundles

Hodge–Newton decompositions of reductive monoids

A section of those articles are designed to function a self-contained advent to those subject matters, whereas the remainder contributions are examine articles containing formerly unpublished effects, that are certain to develop into very influential for destiny paintings. between those, for instance, the $64000 contemporary 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 concept, algebraic combinatorics and the speculation of algebraic staff embeddings will take advantage of this detailed and vast compilation of a few primary leads to (semi)group conception, algebraic workforce embeddings and algebraic combinatorics merged less than the umbrella of algebraic monoids.

Show description

Read or Download Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics PDF

Best combinatorics books

Introduction to combinatorial maps - download pdf or read online

Maps as a mathematical major subject arose most likely from the 4 colour challenge and the extra basic map coloring challenge within the mid of the 19th century. writer couldn't checklist even major references on them since it is widely known for mathematicians and past the scope of this lecture notes. right here, writer in simple terms intends to give a accomplished thought of combinatorial maps as a rigorous mathematical idea which has been built in basic terms in contemporary few many years.

Theodore G Faticoni's Combinatorics : an introduction PDF

Bridges combinatorics and likelihood and uniquely comprises exact formulation and proofs to advertise mathematical thinkingCombinatorics: An advent introduces readers to counting combinatorics, deals examples that characteristic special ways and ideas, and offers case-by-case equipment for fixing difficulties.

Download PDF by Ian Anderson: A first course in combinatorial mathematics

Now in a brand new moment variation, this quantity offers a transparent and concise therapy of an more and more very important department of arithmetic. a different introductory survey whole with easy-to-understand examples and pattern difficulties, this article comprises info on such easy combinatorial instruments as recurrence relatives, producing features, occurrence matrices, and the non-exclusion precept.

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

Example text

G1 g2 ; g2 1 y1 g2 y2 / 24 M. 1G ; 1N / (this defines the semi-direct product of G with N ). gh 1 ; hy/: In other words, ' W M ! G=H identifies M to the fiber bundle G H N ! G=H associated to the principal H -bundle G ! G=H and to the variety N on which H acts by left multiplication. We say that the algebraic monoid M is induced from N . If we no longer assume that H is an algebraic group, then N is just a submonoid scheme of M , and the above properties hold in the setting of monoid schemes. We now obtain slightly weaker versions of these properties in the setting of algebraic monoids.

It follows that X is reduced. But X Š G N and hence N is reduced. If in addition H is connected, then the fibers of are irreducible; hence the same holds for 0 , and X is irreducible. As above, it follows that N is irreducible. o o (ii) Consider the reduced neutral component Hred  H ; then Hred is a closed o normal subgroup of G. Moreover, the natural map ı W G=Hred ! G=H is a finite morphism and sits in a commutative square G ? y o G=Hred à ı ! M ? 'y ! G=H; On Algebraic Semigroups and Monoids 23 o where à denotes the inclusion.

M is a finite birational homomorphism of algebraic monoids. Maff /. 28 M. Brion (v) M is normal if and only if Maff is normal and Ä is an isomorphism. Then the assignment I 7! I \ Maff defines a bijection between the two-sided ideals of M and those of Maff ; the inverse bijection is given by J 7! GJ . Maff /. Proof. Maff / contains Gaff as an open subgroup. Maff / D Gaff . Hence Maff is affine by Theorem 2. (ii) The assertion follows readily from the Rosenlicht decomposition: since Gaff \ Gant is contained in the center of Gaff , its action on Maff by conjugation is trivial.

Download PDF sample

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


by Edward
4.1

Rated 4.10 of 5 – based on 40 votes