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Index Theory on Graphs: Graph-Index and Extended Jones Index of von Neumann Algebras Induced by Graphs - Softcover

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9783639332711: Index Theory on Graphs: Graph-Index and Extended Jones Index of von Neumann Algebras Induced by Graphs
Softcover
ISBN 10: 3639332717 ISBN 13: 9783639332711
Verlag: VDM Verlag Dr. Müller, 2011

Inhaltsangabe

In this monograph, we study the relation between graph-index and Watatani's extended Jones index of certain von Neumann algebras. This research provides not only interesting examples of Jones index theory but also the connection between combinatorics (graph theory), algebra (grouopoid theory), operator algebra, and noncommutative dynamical systems. Moreover, the study of graph-index, itself, is an interesting topic in graph theory because these quantities give invariants for quotient structures induced by graphs. We first define the indexes (or the index numbers) of graph inclusions, which are determined by corresponding subgroupoid inclusions. We call them graph-indexes (of graph inclusions). If we take a special graph inclusion, a vertex-full subgraph inclusion, then our graph-index has close connection with Watatani's extended Jones index. We show that Jones indexes of von-Neumann algebra- inclusions are characterized by our graph-indexes, and vice versa, whenever von Neumann algebras are generated by groupoids of graphs. This characterization will be extended to the case where we have graph-groupoid dynamical systems.

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Verlag
VDM Verlag Dr. Müller
Erscheinungsdatum
2011
Sprache
Englisch
ISBN 10 
3639332717
ISBN 13 
9783639332711
Einband
Taschenbuch
Anzahl der Seiten
136
Kontakt zum Hersteller
Editions Muse
customerservice@vdm-vsg.de

Brivibas gatve 197
Riga
1039
Lettland