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

The Index Semigroup Induced by Finite Trees | Index Morphisms and Classification of von Neumann Algebras Induced by Finite Trees | Ilwoo Cho | Taschenbuch | 88 S. | Englisch | 2011 | LAP LAMBERT Academic Publishing | EAN 9783846590157 | Verantwortliche Person für die EU: BoD - Books on Demand, In de Tarpen 42, 22848 Norderstedt, info[at]bod[dot]de | Anbieter: preigu. Seller Inventory # 106706581

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

Bibliographic Details

Title: The Index Semigroup Induced by Finite Trees ...
Publisher: LAP LAMBERT Academic Publishing
Publication Date: 2011
Binding: Taschenbuch
Condition: Neu