The Index Semigroup Induced by Finite Trees | Index Morphisms and Classification of von Neumann Algebras Induced by Finite Trees

Ilwoo Cho

ISBN 10: 3846590150 ISBN 13: 9783846590157

Published by LAP LAMBERT Academic Publishing, 2011

Language: English

Condition: New Soft cover

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Bibliographic Details

Title

The Index Semigroup Induced by Finite Trees | Index Morphisms and Classification of von Neumann Algebras Induced by Finite Trees

Publisher

LAP LAMBERT Academic Publishing

Publication Date

2011

Language

English

ISBN 10

3846590150

ISBN 13

9783846590157

Binding

Taschenbuch

Condition

Neu

Dimensions

Weight

149 grams

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About this title

Synopsis

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.

About the Author

Master Degrees: Sungkyunkwan University and University of Iowa (Math) / Ph.D : University of Iowa (Math) / Current Position: Assistant Professor in Saint Ambrose University

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