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Author : Mark V. Lawson
Publisher : World Scientific
Page : 430 pages
File Size : 54,7 Mb
Release : 1998
Category : Mathematics
ISBN : 9810233167
"this volume represents an outstanding contribution to the field. The resolute graduate student or mature researcher, alike, can find a wealth of directions for future work".Mathematical Reviews
Author : Mark V Lawson
Publisher : World Scientific
Page : 428 pages
File Size : 48,9 Mb
Release : 1998-11-06
Category : Mathematics
ISBN : 9789814496711
Symmetry is one of the most important organising principles in the natural sciences. The mathematical theory of symmetry has long been associated with group theory, but it is a basic premise of this book that there are aspects of symmetry which are more faithfully represented by a generalization of groups called inverse semigroups. The theory of inverse semigroups is described from its origins in the foundations of differential geometry through to its most recent applications in combinatorial group theory, and the theory tilings. Contents:Introduction to Inverse SemigroupsExtending Partial SymmetriesThe Natural Partial OrderOrdered GroupoidsExtensions of Inverse SemigroupsFree Inverse SemigroupsE-unitary Inverse SemigroupsEnlargements0-E-unitary Inverse SemigroupsCategory Actions and Inverse Semigroups Readership: Mathematicians, and students of symmetry in the physical sciences. keywords:Semigroup Theory;Inverse Semigroup Theory;Category Theory;Groupoids;Ordered Groupoids;Cateory Actions;Symmetry;Partial Symmetry;Pseudogroups;Topological Groupoids “… this volume represents an outstanding contribution to the field. The resolute graduate student or mature researcher, alike, can find a wealth of directions for future work.” Mathematical Reviews
Author : Alan Paterson
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217749
In recent years, it has become increasingly clear that there are important connections relating three concepts -- groupoids, inverse semigroups, and operator algebras. There has been a great deal of progress in this area over the last two decades, and this book gives a careful, up-to-date and reasonably extensive account of the subject matter. After an introductory first chapter, the second chapter presents a self-contained account of inverse semigroups, locally compact and r-discrete groupoids, and Lie groupoids. The section on Lie groupoids in chapter 2 contains a detailed discussion of groupoids particularly important in noncommutative geometry, including the holonomy groupoids of a foliated manifold and the tangent groupoid of a manifold. The representation theories of locally compact and r-discrete groupoids are developed in the third chapter, and it is shown that the C*-algebras of r-discrete groupoids are the covariance C*-algebras for inverse semigroup actions on locally compact Hausdorff spaces. A final chapter associates a universal r-discrete groupoid with any inverse semigroup. Six subsequent appendices treat topics related to those covered in the text. The book should appeal to a wide variety of professional mathematicians and graduate students in fields such as operator algebras, analysis on groupoids, semigroup theory, and noncommutative geometry. It will also be of interest to mathematicians interested in tilings and theoretical physicists whose focus is modeling quasicrystals with tilings. An effort has been made to make the book lucid and 'user friendly"; thus it should be accessible to any reader with a basic background in measure theory and functional analysis.
Author : Friedrich Wehrung
Publisher : Springer
Page : 242 pages
File Size : 45,6 Mb
Release : 2017-09-09
Category : Mathematics
ISBN : 9783319615998
Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings. This is done via the study of a monoid invariant, defined on Boolean inverse semigroups, called the type monoid. The new techniques contrast with the currently available topological approaches. Many positive results, but also many counterexamples, are provided.
Author : Stephen Lipscomb
Publisher : American Mathematical Soc.
Page : 187 pages
File Size : 43,9 Mb
Release : 1996
Category : Inverse semigroups
ISBN : 9780821806272
With over 60 figures, tables, and diagrams, this text is both an intuitive introduction to and a rigorous study of finite symmetric inverse semigroups. The book presents much of the material on the theory of finite symmetric inverse semigroups, unifying the classical finite symmetric group theory with its semigroup analogue. A comment section at the end of each chapter provides new historical perspective. New proofs, new theorems and the use of multiple figures, tables, and diagrams to present complex ideas make this book current and highly readable.
Author : Mario Petrich
Publisher : Wiley-Interscience
Page : 696 pages
File Size : 53,6 Mb
Release : 1984
Category : Mathematics
ISBN : UCAL:B4980283
Author : Ben Silver
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 49,5 Mb
Release : 1988-12-31
Category : Mathematics
ISBN : 0821895753
This volume contains papers selected by leading specialists in algebraic semigroups in the U.S., the United Kingdom, and Australia. Many of the papers strongly influenced the development of algebraic semigroups, but most were virtually unavailable outside the U.S.S.R. Written by some of the most prominent Soviet researchers in the field, the papers have a particular emphasis on semigroups of transformations. Boris Schein of the University of Arkansas is the translator.
Author : Gracinda M S Gomes,Isabel M Araujo,Mario J J Branco,Vitor H Fernandes
Publisher : World Scientific
Page : 260 pages
File Size : 40,9 Mb
Release : 2004-07-14
Category : Mathematics
ISBN : 9789814482325
In recent years, semigroups and languages have seen huge developments and found their motivation in other fields of mathematics as well as in computer science. This book is a collection of original contributions in those fields.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Author : Isabel M. Ara£jo
Publisher : World Scientific
Page : 296 pages
File Size : 40,7 Mb
Release : 2004
Category : Computers
ISBN : 981270261X
In recent years, semigroups and languages have seen huge developments and found their motivation in other fields of mathematics as well as in computer science. This book is a collection of original contributions in those fields. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences."
Author : T. E. Hall,P. R. Jones,G. B. Preston
Publisher : Academic Press
Page : 266 pages
File Size : 45,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483267333
Semigroups is a collection of papers dealing with models of classical statistics, sequential computing machine, inverse semi-groups. One paper explains the structure of inverse semigroups that leads to P-semigroups or E-unitary inverse semigroups by utilizing the P-theorem of W.D. Nunn. Other papers explain the characterization of divisibility in the category of sets in terms of images and relations, as well as the universal aspects of completely simple semigroups, including amalgamation, the lattice of varieties, and the Hopf property. Another paper explains finite semigroups which are extensions of congruence-free semigroups, where their set of congruences forms a chain. The paper then shows how to construct such semigroups. A finite semigroup (which is decomposable into a direct product of cyclic semigroups which are not groups) is actually uniquely decomposable. One paper points out when a finite semigroup has such a decomposition, and how its non-group cyclic direct factors, if any, can be found. The collection can prove useful for mathematicians, statisticians, students, and professors of higher mathematics or computer science.
Author : Jorge Almeida,Gabriela Bordalo,Philip Dwinger
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 49,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489926081
This volume contains papers which, for the most part, are based on talks given at an international conference on Lattices, Semigroups, and Universal Algebra that was held in Lisbon, Portugal during the week of June 20-24, 1988. The conference was dedicated to the memory of Professor Antonio Almeida Costa, a Portuguese mathematician who greatly contributed to the development of th algebra in Portugal, on the 10 anniversary of his death. The themes of the conference reflect some of his research interests and those of his students. The purpose of the conference was to gather leading experts in Lattices, Semigroups, and Universal Algebra and to promote a discussion of recent developments and trends in these areas. All three fields have grown rapidly during the last few decades with varying degrees of interaction. Lattice theory and Universal Algebra have historically evolved alongside with a large overlap between the groups of researchers in the two fields. More recently, techniques and ideas of these theories have been used extensively in the theory of semigroups. Conversely, some developments in that area may inspire further developments in Universal Algebra. On the other hand, techniques of semi group theory have naturally been employed in the study of semilattices. Several papers in this volume elaborate on these interactions.
Author : P G Romeo,John. C Meakin,A R Rajan
Publisher : Springer
Page : 218 pages
File Size : 46,8 Mb
Release : 2015-07-06
Category : Mathematics
ISBN : 9788132224884
This book discusses recent developments in semigroup theory and its applications in areas such as operator algebras, operator approximations and category theory. All contributing authors are eminent researchers in their respective fields, from across the world. Their papers, presented at the 2014 International Conference on Semigroups, Algebras and Operator Theory in Cochin, India, focus on recent developments in semigroup theory and operator algebras. They highlight current research activities on the structure theory of semigroups as well as the role of semigroup theoretic approaches to other areas such as rings and algebras. The deliberations and discussions at the conference point to future research directions in these areas. This book presents 16 unpublished, high-quality and peer-reviewed research papers on areas such as structure theory of semigroups, decidability vs. undecidability of word problems, regular von Neumann algebras, operator theory and operator approximations. Interested researchers will find several avenues for exploring the connections between semigroup theory and the theory of operator algebras.
Author : Jorge M. Andre
Publisher : World Scientific
Page : 288 pages
File Size : 44,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812708700
This festschrift volume in honour of Donald B McAlister on the occasion of his 65th birthday presents papers from leading researchers in semigroups and formal languages. The contributors cover a number of areas of current interest: from pseudovarieties and regular languages to ordered groupoids and one-relator groups, and from semigroup algebras to presentations of monoids and transformation semigroups. The papers are accessible to graduate students as well as researchers seeking new directions for future work.
Author : Alfred Hoblitzelle Clifford,Arthur Hoblitzelle Clifford,G. B. Preston
Publisher : American Mathematical Soc.
Page : 352 pages
File Size : 45,7 Mb
Release : 1961
Category : Mathematics
ISBN : 9780821802724
Author : Gracinda M. S. Gomes,Jean Eric Pin,Pedro V. Silva
Publisher : World Scientific
Page : 536 pages
File Size : 50,5 Mb
Release : 2002
Category : Mathematics
ISBN : 9812776885
The thematic term on OC Semigroups, Algorithms, Automata and LanguagesOCO organized at the International Centre of Mathematics (Coimbra, Portugal) in MayOCoJuly 2001 was the gathering point for researchers working in the field of semigroups, algorithms, automata and languages. These areas were selected considering their huge recent developments, their potential applications, and the motivation from other fields of mathematics and computer science. This proceedings volume is a unique collection of advanced courses and original contributions on semigroups and their connections with logic, automata, languages, group theory, discrete dynamics, topology and complexity. A selection of open problems discussed during the thematic term is also included. Contents: Finite Semigroups: An Introduction to a Unified Theory of Pseudovarieties (J Almeida); On Existence Varieties of Regular Semigroups (K Auinger); Varieties of Languages (M J J Branco); A Short Introduction to Automatic Group Theory (C Choffrut); Some Results on Semigroup-Graded Rings (W D Munn); Profinite Groups and Applications to Finite Semigroups (L Ribes); Dynamics of Finite Semigroups (J Almeida); Finite Semigroups Imposing Tractable Constraints (A Bulatov et al.); On the Efficiency and Deficiency of Rees Matrix Semigroups (C M Campbell et al.); Some Pseudovariety Joins Involving Groups and Locally Trivial Semigroups (J C Costa); Partial Action of Groups on Relational Structures: A Connection Between Model Theory and Profinite Topology (T Coulbois); Some Relatives of Automatic and Hyperbolic Groups (M Hoffmann et al.); A Sampler of a Topological Approach to Inverse Semigroups (B Steinberg); Finite Semigroups and the Logical Description of Regular Languages (H Straubing); Diamonds are Forever: The Variety DA (P Tesson & D Th(r)rien); Decidability Problems in Finite Semigroups (P G Trotter); and other papers. Readership: Researchers, academics and graduate students in pure mathematics and computer science."