Graph Algebras

Author : Iain Raeburn
Publisher : American Mathematical Soc.
ISBN 13 : 0821836609
Total Pages : 130 pages
Book Rating : 4.06/5 ( download)

DOWNLOAD NOW!

Download or read book Graph Algebras written by Iain Raeburn and published by American Mathematical Soc.. This book was released on 2005 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph algebras are a family of operator algebras which are associated to directed graphs. These algebras have an attractive structure theory in which algebraic properties of the algebra are related to the behavior of paths in the underlying graph. In the past few years there has been a great deal of activity in this area, and graph algebras have cropped up in a surprising variety of situations, including non-abelian duality, non-commutative geometry, and the classification of simple $C*$-algebras. The first part of the book provides an introduction to the subject suitable for students who have seen a first course on the basics of $C*$-algebras. In the second part, the author surveys the literature on the structure theory of graph algebras, highlights some applications of this theory, and discusses several recent generalizations which seem particularly promising. The volume is suitable for graduate students and research mathematicians interested in graph theory and operator algebras.

Author : Andrei Kelarev
Publisher : CRC Press
ISBN 13 : 9780824747084
Total Pages : 388 pages
Book Rating : 4.89/5 ( download)

DOWNLOAD NOW!

Download or read book Graph Algebras and Automata written by Andrei Kelarev and published by CRC Press. This book was released on 2003-07-08 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph algebras possess the capacity to relate fundamental concepts of computer science, combinatorics, graph theory, operations research, and universal algebra. They are used to identify nontrivial connections across notions, expose conceptual properties, and mediate the application of methods from one area toward questions of the other four. After a concentrated review of the prerequisite mathematical background, Graph Algebras and Automata defines graph algebras and reveals their applicability to automata theory. It proceeds to explore assorted monoids, semigroups, rings, codes, and other algebraic structures and to outline theorems and algorithms for finite state automata and grammars.

Author : Ilwoo Cho
Publisher : CRC Press
ISBN 13 : 146659019X
Total Pages : 446 pages
Book Rating : 4.99/5 ( download)

DOWNLOAD NOW!

Download or read book Algebras, Graphs and their Applications written by Ilwoo Cho and published by CRC Press. This book was released on 2013-09-11 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory connected with discrete and combinatorial mathematical objects. It also covers tools and methods from a variety of mathematical areas, including algebra, operator theory, and combinatorics, and offers numerous applications of fractal theory, entropy theory, K-theory, and index theory.

Author : Ilwoo Cho
Publisher : CRC Press
ISBN 13 : 1466590203
Total Pages : 442 pages
Book Rating : 4.05/5 ( download)

DOWNLOAD NOW!

Download or read book Algebras, Graphs and their Applications written by Ilwoo Cho and published by CRC Press. This book was released on 2013-09-11 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory connected with discrete and combinatorial mathematic

Author : Frederick M. Goodman
Publisher : Springer Science & Business Media
ISBN 13 : 1461396417
Total Pages : 297 pages
Book Rating : 4.13/5 ( download)

DOWNLOAD NOW!

Download or read book Coxeter Graphs and Towers of Algebras written by Frederick M. Goodman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: A recent paper on subfactors of von Neumann factors has stimulated much research in von Neumann algebras. It was discovered soon after the appearance of this paper that certain algebras which are used there for the analysis of subfactors could also be used to define a new polynomial invariant for links. Recent efforts to understand the fundamental nature of the new link invariants has led to connections with invariant theory, statistical mechanics and quantum theory. In turn, the link invariants, the notion of a quantum group, and the quantum Yang-Baxter equation have had a great impact on the study of subfactors. Our subject is certain algebraic and von Neumann algebraic topics closely related to the original paper. However, in order to promote, in a modest way, the contact between diverse fields of mathematics, we have tried to make this work accessible to the broadest audience. Consequently, this book contains much elementary expository material.

Author : Ravindra B. Bapat
Publisher : Springer
ISBN 13 : 1447165691
Total Pages : 197 pages
Book Rating : 4.99/5 ( download)

DOWNLOAD NOW!

Download or read book Graphs and Matrices written by Ravindra B. Bapat and published by Springer. This book was released on 2014-09-19 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.

Author : Ibrahim Assem
Publisher : Springer
ISBN 13 : 3319745859
Total Pages : 223 pages
Book Rating : 4.55/5 ( download)

DOWNLOAD NOW!

Download or read book Homological Methods, Representation Theory, and Cluster Algebras written by Ibrahim Assem and published by Springer. This book was released on 2018-04-18 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study. The six mini-courses comprising this text were delivered March 7–18, 2016 at a CIMPA (Centre International de Mathématiques Pures et Appliquées) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck. The courses held were: Advanced homological algebra Introduction to the representation theory of algebras Auslander-Reiten theory for algebras of infinite representation type Cluster algebras arising from surfaces Cluster tilted algebras Cluster characters Introduction to K-theory Brauer graph algebras and applications to cluster algebras

Author : Reiko Heckel
Publisher : Springer
ISBN 13 : 3319753967
Total Pages : 333 pages
Book Rating : 4.66/5 ( download)

DOWNLOAD NOW!

Download or read book Graph Transformation, Specifications, and Nets written by Reiko Heckel and published by Springer. This book was released on 2018-02-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume pays tribute to the scientific achievements of Hartmut Ehrig, who passed away in March 2016. The contributions represent a selection from a symposium, held in October 2016 at TU Berlin, commemorating Hartmut’ s life and work as well as other invited papers in the areas he was active in. These areas include Graph Transformation, Model Transformation, Concurrency Theory, in particular Petri Nets, Algebraic Specification, and Category Theory in Computer Science.

Author : Yemon Choi
Publisher : Springer Nature
ISBN 13 : 3031380207
Total Pages : 262 pages
Book Rating : 4.04/5 ( download)

DOWNLOAD NOW!

Download or read book Operators, Semigroups, Algebras and Function Theory written by Yemon Choi and published by Springer Nature. This book was released on 2023-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.

Author : Bruno Courcelle
Publisher : Cambridge University Press
ISBN 13 : 0521898331
Total Pages : 743 pages
Book Rating : 4.31/5 ( download)

DOWNLOAD NOW!

Download or read book Graph Structure and Monadic Second-Order Logic written by Bruno Courcelle and published by Cambridge University Press. This book was released on 2012-06-14 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.