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Graph Algebras

2005 Mathematics
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Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 609/5 ( reviews)

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Book Synopsis Graph Algebras by : Iain Raeburn

Download or read book Graph Algebras written by Iain Raeburn. This book was released on 2005. 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.

Graph Algebras and Automata

2003-07-08 Mathematics
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Release : 2003-07-08
Genre : Mathematics
Kind : eBook
Book Rating : 084/5 ( reviews)

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Book Synopsis Graph Algebras and Automata by : Andrei Kelarev

Download or read book Graph Algebras and Automata written by Andrei Kelarev. This book was released on 2003-07-08. 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.

Algebras, Graphs and their Applications

2013-09-11 Mathematics
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Release : 2013-09-11
Genre : Mathematics
Kind : eBook
Book Rating : 203/5 ( reviews)

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Book Synopsis Algebras, Graphs and their Applications by : Ilwoo Cho

Download or read book Algebras, Graphs and their Applications written by Ilwoo Cho. This book was released on 2013-09-11. 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

Homological Methods, Representation Theory, and Cluster Algebras

2018-04-18 Mathematics
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Release : 2018-04-18
Genre : Mathematics
Kind : eBook
Book Rating : 859/5 ( reviews)

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Book Synopsis Homological Methods, Representation Theory, and Cluster Algebras by : Ibrahim Assem

Download or read book Homological Methods, Representation Theory, and Cluster Algebras written by Ibrahim Assem. This book was released on 2018-04-18. 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

Graph Transformation, Specifications, and Nets

2018-02-06 Computers
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Release : 2018-02-06
Genre : Computers
Kind : eBook
Book Rating : 967/5 ( reviews)

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Book Synopsis Graph Transformation, Specifications, and Nets by : Reiko Heckel

Download or read book Graph Transformation, Specifications, and Nets written by Reiko Heckel. This book was released on 2018-02-06. 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.

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