By Mahir Can, Zhenheng Li, Benjamin Steinberg, Qiang Wang
This booklet includes 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 offered include:
structure and illustration thought of reductive algebraic monoids
monoid schemes and functions of monoids
monoids on the topic of Lie theory
equivariant embeddings of algebraic groups
constructions and houses of monoids from algebraic combinatorics
endomorphism monoids brought about from vector bundles
Hodge–Newton decompositions of reductive monoids
A component to those articles are designed to function a self-contained creation to those subject matters, whereas the remainder contributions are examine articles containing formerly unpublished effects, that are guaranteed to develop into very influential for destiny paintings. between those, for instance, the $64000 contemporary paintings of Michel Brion and Lex Renner displaying 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 reap the benefits of this distinctive and wide compilation of a few primary ends up in (semi)group conception, algebraic crew embeddings and algebraic combinatorics merged below the umbrella of algebraic monoids.
Read or Download Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics PDF
Similar combinatorics books
In a couple of recognized works, M. Kac confirmed that numerous tools of chance thought might be fruitfully utilized to big difficulties of research. The interconnection among likelihood and research additionally performs a critical position within the current publication. even if, our procedure is principally in response to the appliance of study equipment (the approach to operator identities, vital equations conception, twin structures, integrable equations) to likelihood conception (Levy approaches, M.
As soon as the privilege of a mystery few, cryptography is now taught at universities all over the world. creation to Cryptography with Open-Source software program illustrates algorithms and cryptosystems utilizing examples and the open-source computing device algebra procedure of Sage. the writer, a famous educator within the box, presents a hugely functional studying event through progressing at a steady speed, preserving arithmetic at a practicable point, and together with a number of end-of-chapter workouts.
This booklet constitutes the refereed court cases of the tenth overseas convention on Combinatorics on phrases, phrases 2015, held in Kiel, Germany, in September 2015 lower than the auspices of the EATCS. The 14 revised complete papers offered have been rigorously reviewed and chosen from 22 submissions. the most item within the contributions are phrases, finite or endless sequences of symbols over a finite alphabet.
- A Path to Combinatorics for Undergraduates: Counting Strategies
- Combinatorial Convexity and Algebraic Geometry
- Boolean Algebras in Analysis
- Combinatorial Optimization Theory and Algorithms
- Information Security, Coding Theory and Related Combinatorics: Information Coding and Combinatorics - Volume 29 NATO Science for Peace and Security Series
- Moral Calculations: Game Theory, Logic, and Human Frailty
Extra info for Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics
Iii) The above map ' is the universal homomorphism to an algebraic group. On Algebraic Semigroups and Monoids 41 Proof. (i) By Proposition 3 (iii), it suffices to show that e is the unique idempotent of eSe. eSe/, then xy D xf y for all x; y 2 S , by Lemma 2. Taking x D y D e yields e D ef e D f . eye/ for all x; y 2 S . (iii) Let G be an algebraic group and let W S ! G be a homomorphism of algebraic semigroups. exe/ for all x 2 S . Thus, factors uniquely as the homomorphism ' followed by some homomorphism of algebraic groups eSe !
Then X has a structure of algebraic monoid with unit group G if and only if the Albanese morphism ˛ W X ! X / is affine. Proof. In view of Proposition 16, it suffices to show that X is an algebraic monoid if ˛ is affine. X /. X / Š G=K equivariantly for the left (or right) action of G. G/ Y ! G/; for the left (or right) G-action, this yields the fiber bundle G K Y ! G=K. Since ˛ is affine, so is Y . G/ by conjugation. Thus, the group scheme K is quasi-affine, and hence is affine. We now show that the group law K W K K !
On Algebraic Semigroups and Monoids 37 Step 1: we show that every idempotent of S is either a neutral or a zero element. S /. Since Se is a closed irreducible subvariety of S , it is either the whole S or a single point; in the latter case, Se D feg. Thus, one of the following cases occurs: (i) Se D eS D S . , e is the neutral element. (ii) Se D feg and eS D S . Then for any x; y 2 S , we have xe D e and ey D y. Thus, xy D xey D ey D y. So D r in the notation of Example 1 (i), a contradiction since is assumed to be nontrivial.