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Index Theory on Graphs
Graph-Index and Extended Jones Index of von Neumann Algebras Induced by Graphs
Ilwoo Cho
Livre broché | Anglais
58,45 €
+ 116 points
Description
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.
Spécifications
Parties prenantes
- Auteur(s) :
- Editeur:
Contenu
- Nombre de pages :
- 136
- Langue:
- Anglais
Caractéristiques
- EAN:
- 9783639332711
- Date de parution :
- 15-02-11
- Format:
- Livre broché
- Format numérique:
- Trade paperback (VS)
- Dimensions :
- 152 mm x 229 mm
- Poids :
- 208 g
