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The Index Semigroup Induced by Finite Trees: Index Morphisms and Classification of Von Neumann Algebras Induced by Finite Trees Ilwoo Cho
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The Index Semigroup Induced by Finite Trees: Index Morphisms and Classification of Von Neumann Algebras Induced by Finite Trees
Ilwoo Cho
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.
| Mídia | Livros Paperback Book (Livro de capa flexível e brochura) |
| Lançado | 1 de dezembro de 2011 |
| ISBN13 | 9783846590157 |
| Editoras | LAP LAMBERT Academic Publishing |
| Páginas | 88 |
| Dimensões | 150 × 5 × 226 mm · 149 g |
| Idioma | Alemão |
