Graph Groupoids and Partial Isometries

Ilwoo Cho

ISBN 10: 3838313976 / ISBN 13: 9783838313979

Verlag: LAP LAMBERT Academic Publishing Mai 2010, 2010

Beschreibung

This item is printed on demand - it takes 3-4 days longer - Neuware -In this monograph, we consider the connection between graphs and Hilbert space operators. In particular, we are interested in the algebraic structures, called graph groupoids, embedded in operator algebras. In Part 1, we consider the connection from graphs to partial isometries. Every element in graph groupoids assigns an operator, which is either a partial isometry or a projection, under suitable representations. The von Neumann algebras induced by the dynamical systems of graph groupoids are characterized. In Part 2, we observe the connection from partial isometries to graphs. We show that a finite family of partial isometries on a fixed Hilbert space H creates the corresponding graph, and the graph groupoid of it is an embedded groupoid inside B(H). Moreover, the C -subalgebra generated by the family is -isomorphic to the groupoid algebra generated by the graph groupoid of the corresponding graph. As application, we consider the C -subalagebras generated by a single operator. 92 pp. Englisch.

Bestandsnummer des Verkäufers 9783838313979

Bibliografische Details

• Titel: Graph Groupoids and Partial Isometries
• Verlag: LAP LAMBERT Academic Publishing Mai 2010
• Erscheinungsjahr: 2010
• Sprache: Englisch
• ISBN-10: 3838313976
• ISBN-13: 9783838313979
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 220B x 150 H x 6 T Millimeter Breite: 220 mm, Höhe: 150 mm, Tiefe: 6 mm
• Gewicht: 155 Gramm

Über diesen Titel

Inhaltsangabe

In this monograph, we consider the connection between graphs and Hilbert space operators. In particular, we are interested in the algebraic structures, called graph groupoids, embedded in operator algebras. In Part 1, we consider the connection from graphs to partial isometries. Every element in graph groupoids assigns an operator, which is either a partial isometry or a projection, under suitable representations. The von Neumann algebras induced by the dynamical systems of graph groupoids are characterized. In Part 2, we observe the connection from partial isometries to graphs. We show that a finite family of partial isometries on a fixed Hilbert space H creates the corresponding graph, and the graph groupoid of it is an embedded groupoid inside B(H). Moreover, the C*-subalgebra generated by the family is *-isomorphic to the groupoid algebra generated by the graph groupoid of the corresponding graph. As application, we consider the C*-subalagebras generated by a single operator.