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The Index Semigroup Induced by Finite Trees


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  • Product Description

In this monograph, we study graph-index, Watatani's extended Jones index, and the relations between them. From this investigation, we realize that graph-index of graphs and Jones index of von Neumann algebras generated by "graph groupoids" are equivalent in a certain sense, whenver given graphs are finite trees. We provides the classification of graph-groupoid von Neumann algebras induced by finite trees with respect to these equivalent indexes. By understanding the indexings as morphisms, we establish actions of morphisms and construct the corresponding algebraic structure, called the "index semigroup." We study the fundamental properties of them. As application, we consider the connection between our index semigroup and K-groups of finite-tree-groupoid von Neumann algebras.

Product Specifications
SKU :COC93710
Number of Pages88
Publishing Year2011-12-01T00:00:00.000
Edition1 st
Book TypeMathematics
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-08-14 00:00:00
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