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Index Theory on Graphs

 

Marketed By :  VDM Verlag Dr. Müller   Sold By :  Kamal Books International  
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  • Product 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.

Product Specifications
SKU :COC93513
AuthorILWOO CHO
LanguageEnglish
BindingPaperback
Number of Pages136
Publishing Year2011-02-15T00:00:00.000
ISBN978-3639332711
Edition1 st
Book TypeMathematics
Country of ManufactureIndia
Product BrandVDM Verlag Dr. Müller
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-08-14 00:00:00