The Index Semigroup Induced by Finite Trees (Paperback)

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.

General

Imprint:	Lap Lambert Academic Publishing
Country of origin:	Germany
Release date:	December 2011
First published:	December 2011
Authors:	Ilwoo Cho
Dimensions:	229 x 152 x 5mm (L x W x T)
Format:	Paperback - Trade
Pages:	88
ISBN-13:	978-3-8465-9015-7
Categories:	Books > Science & Mathematics > Mathematics > General
LSN:	3-8465-9015-0
Barcode:	9783846590157

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