Download or read book Algebraic Monoids Group Embeddings and Algebraic Combinatorics written by Mahir Can and published by Springer. This book was released on 2014-06-11 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: structure and representation theory of reductive algebraic monoids monoid schemes and applications of monoids monoids related to Lie theory equivariant embeddings of algebraic groups constructions and properties of monoids from algebraic combinatorics endomorphism monoids induced from vector bundles Hodge–Newton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semi groups are strongly π-regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics and the theory of algebraic group embeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings and algebraic combinatorics merged under the umbrella of algebraic monoids.
Download or read book Advances in Algebra written by Jörg Feldvoss and published by Springer. This book was released on 2019-02-27 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume covers a range of research topics in algebra from the Southern Regional Algebra Conference (SRAC) that took place in March 2017. Presenting theory as well as computational methods, featured survey articles and research papers focus on ongoing research in algebraic geometry, ring theory, group theory, and associative algebras. Topics include algebraic groups, combinatorial commutative algebra, computational methods for representations of groups and algebras, group theory, Hopf-Galois theory, hypergroups, Lie superalgebras, matrix analysis, spherical and algebraic spaces, and tropical algebraic geometry. Since 1988, SRAC has been an important event for the algebra research community in the Gulf Coast Region and surrounding states, building a strong network of algebraists that fosters collaboration in research and education. This volume is suitable for graduate students and researchers interested in recent findings in computational and theoretical methods in algebra and representation theory.
Download or read book Linear Algebraic Monoids written by Lex E. Renner and published by Springer Science & Business Media. This book was released on 2005-03-11 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of linear algebraic monoids culminates in a coherent blend of algebraic groups, convex geometry, and semigroup theory. The book discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. An explicit cell decomposition is constructed for the wonderful compactification, as is a universal deformation for any semisimple group. A final chapter summarizes important connections with other areas of algebra and geometry. The book will serve as a solid basis for further research. Open problems are discussed as they arise and many useful exercises are included.
Download or read book Representation Theory of Finite Monoids written by Benjamin Steinberg and published by Springer. This book was released on 2016-12-09 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields. Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional algebras. The content is divided into 7 parts. Part I consists of 3 preliminary chapters with no prior knowledge beyond group theory assumed. Part II forms the core of the material giving a modern module-theoretic treatment of the Clifford –Munn–Ponizovskii theory of irreducible representations. Part III concerns character theory and the character table of a monoid. Part IV is devoted to the representation theory of inverse monoids and categories and Part V presents the theory of the Rhodes radical with applications to triangularizability. Part VI features 3 chapters devoted to applications to diverse areas of mathematics and forms a high point of the text. The last part, Part VII, is concerned with advanced topics. There are also 3 appendices reviewing finite dimensional algebras, group representation theory, and Möbius inversion.
Download or read book Linear Algebraic Monoids written by Lex E. Renner and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This solid volume discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. Open problems are discussed as they arise and many useful exercises are included.
Download or read book Algebraic Graph Theory written by Ulrich Knauer and published by Walter de Gruyter. This book was released on 2011-09-29 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools. They allow to model net structures – like roads, computers, telephones – instances of abstract data structures – like lists, stacks, trees – and functional or object oriented programming. In turn, graphs are models for mathematical objects, like categories and functors. This highly self-contained book about algebraic graph theory is written with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvalues. It ends with a challenging chapter on the topological question of embeddability of Cayley graphs on surfaces.
Download or read book Combinatorial Number Theory and Additive Group Theory written by Alfred Geroldinger and published by Springer Science & Business Media. This book was released on 2009-06-04 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.
Download or read book Groups Combinatorics and Geometry written by A A Ivanov and published by World Scientific. This book was released on 2003-03-19 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past 20 years, the theory of groups — in particular simple groups, finite and algebraic — has influenced a number of diverse areas of mathematics. Such areas include topics where groups have been traditionally applied, such as algebraic combinatorics, finite geometries, Galois theory and permutation groups, as well as several more recent developments. Among the latter are probabilistic and computational group theory, the theory of algebraic groups over number fields, and model theory, in each of which there has been a major recent impetus provided by simple group theory. In addition, there is still great interest in local analysis in finite groups, with substantial new input from methods of geometry and amalgams, and particular emphasis on the revision project for the classification of finite simple groups. This important book contains 20 survey articles covering many of the above developments. It should prove invaluable for those working in the theory of groups and its applications. Contents:Curtis–Phan–Tits Theory (C D Bennett et al.)Derangements in Simple and Primitive Groups (J Fulman & R Guralnick)Computing with Matrix Groups (W M Kantor & Á Seress)Bases of Primitive Permutation Groups (M W Liebeck & A Shalev)Modular Subgroup Arithmetic (T W Müller)Counting Nets in the Monster (S P Norton)Overgroups of Finite Quasiprimitive Permutation Groups (C E Praeger)Old Groups Can Learn New Tricks (L Pyber)Structure and Presentations of Lie-Type Groups (F G Timmesfeld)Computing in the Monster (R A Wilson)and other papers Readership: Graduate students, researchers and academics in algebra. Keywords:Simple Groups;Algebraic Combinatorics;Finite Geometry;Permutation Groups. Probabilistic Group
Download or read book Algebraic Combinatorics Via Finite Group Actions written by Adalbert Kerber and published by . This book was released on 1991 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Graph Theory written by Ulrich Knauer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-10-08 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph models are extremely useful for a large number of applications as they play an important role as structuring tools. They allow to model net structures – like roads, computers, telephones, social networks – instances of abstract data structures – like lists, stacks, trees – and functional or object oriented programming. The focus of this highly self-contained book is on homomorphisms and endomorphisms, matrices and eigenvalues.
Download or read book Groups St Andrews 2005 Volume 2 written by C. M. Campbell and published by Cambridge University Press. This book was released on 2007-01-04 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected papers from 'Groups St Andrews 2005' cover a wide spectrum of modern group theory.
Download or read book Algebraic Combinatorics on Words written by M. Lothaire and published by Cambridge University Press. This book was released on 2002-04-18 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive 2002 introduction to combinatorics on words for mathematicians and theoretical computer scientists.
Download or read book Algorithms and Classification in Combinatorial Group Theory written by Gilbert Baumslag and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume are the result of a workshop held in January 1989 at the Mathematical Sciences Research Institute. Topics covered include decision problems, finitely presented simple groups, combinatorial geometry and homology, and automatic groups and related topics.
Download or read book Combinatorial and Geometric Group Theory written by Oleg Bogopolski and published by Springer Science & Business Media. This book was released on 2011-01-28 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.
Download or read book Algebraic Generalizations of Discrete Groups written by Benjamin Fine and published by CRC Press. This book was released on 1999-07-27 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of one-relator products of cyclics or groups with a single defining relation, extending the algebraic study of Fuchsian groups to the more general context of one-relator products and related group theoretical considerations. It provides a self-contained account of certain natural generalizations of discrete groups.
Download or read book Semigroups and Combinatorial Applications written by Gerard Lallement and published by John Wiley & Sons. This book was released on 1979 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to present those parts of the theory of semigroups that are directly related to automata theory, algebraic linguistics, and combinatorics. Publications in these mathematical disciplines contained methods and results pertaining to the algebraic theory of semigroups, and this has contributed to considerable enrichment of the theory, enlargement of its scope, and improved its potential to become a major domain of algebra. Semigroup theory appears to provide a general framework for unifying and clarifying a number of topics in fields that at first sight appear unrelated. This book is intended as a textbook for graduate students in mathematics and computer science, and as a reference book for researchers interested in associative structures.
Download or read book Non Unique Factorizations written by Alfred Geroldinger and published by Chapman and Hall/CRC. This book was released on 2006-01-13 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory offers a look at the present state of the theory in a single, unified resource. Taking a broad look at the algebraic, combinatorial, and analytic fundamentals, this book derives factorization results and applies them in concrete arithmetical situations using appropriate transfer principles. It begins with a basic introduction that can be understood with knowledge of standard basic algebra. The authors then move to the algebraic theory of monoids, arithmetic theory of monoids, the structure of sets of lengths, additive group theory, arithmetical invariants, and the arithmetic of Krull monoids. They also provide a self-contained introduction to abstract analytic number theory as well as a modern treatment of W. Narkiewicz's analytic theory of non-unique factorizations. Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory builds the discussion from first principles to applied problem solving, making it ideally suited to those not familiar with the theory as well as those who wish to deepen their understanding.
