Algebras, graphs and their applications
 Author/Creator
 Cho, Ilwoo, author.
 Language
 English.
 Publication
 Boca Raton, FL : CRC Press, Taylor & Francis Group, [2014]
 Physical description
 xii, 431 pages : illustrations ; 24 cm
Access
Available online

Stacks

Unknown
QA181 .C46 2014

Unknown
QA181 .C46 2014
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Contributors
 Contributor
 Jørgensen, Palle E. T., 1947 editor.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Preface
 Algebra on graphs
 Representations and operator algebras of graph groupoids
 Operator theory on graphs
 Fractals on graph groupoids
 Entropy theory on graphs
 Jones Index Theory on graph groupoids
 Network theory on graphs
 Ktheory on graphs
 Index.
 Summary
 "In this book, we consider algebra on directed graphs. From combinatorial objects, direct graphs, we establish corresponding algebraic objects which become groupoids. We call such groupoids graph groupoids. Connected with groupoid theory, we investigate the properties of graph groupoids. From this investigation, we can realize that graph groupoids act like the free groups in group theory. In other words, the study of graph groupoids is understood as groupoidal version of freegroup theory. As application, we observe how graph groupoids are playing their role in different mathematical and scientific areas, including general groupoid theory, representation theory, automata theory, operator algebra (von Neumann algebra theory, C*algebra theory, free probability, and index theory), noncommutative dynamical systems (groupoid dynamical systems), operator theory (spectral theory), fractal theory, information theory (entropy theory), and network theory, etc. We can check all operated groupoids (for instance, groupoid sums, product groupoids, quotient groupoids, etc) of graph groupoids are graph groupoids, too. This means that the study of operated groupoids of graph groupoids becomes nothing but studying other graph groupoids. It makes us easy to handle graphgroupoid related structures" Provided by publisher.
 Supplemental links
 Cover image
Subjects
 Subject
 Groupoids.
 Operator theory.
Bibliographic information
 Publication date
 2014
 Responsibility
 Ilwoo Cho ; edited by Palle E.T. Jorgensen.
 ISBN
 9781466590199
 146659019X