Journal article
Directed Graphs, von Neumann Algebras, and Index
Algebras and Representation Theory, Vol.15(1), pp.53-108
02/2012
DOI: 10.1007/s10468-010-9233-7
Abstract
In this paper, we assign index numbers to finite directed graphs. Motivated by the indices of Jones and Watatani (from operator algebra theory), we introduce and compute a new graph-theoretical index, and consider the connection with Watatani’s extended Jones index. Starting with an inclusion of finite directed graphs, we show that there is a natural subgroupoid inclusion, and then a tower of von Neumann algebras. In particular, each step in the tower having the same index number, under certain normalization.
Details
- Title: Subtitle
- Directed Graphs, von Neumann Algebras, and Index
- Creators
- Ilwoo Cho - Department of Mathematics St. Ambrose University 518 W. Locust St. Davenport IA 52803 USAPalle Jorgensen - Department of Mathematics University of Iowa 14 McLean Hall Iowa City IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Algebras and Representation Theory, Vol.15(1), pp.53-108
- Publisher
- Springer Netherlands; Dordrecht
- DOI
- 10.1007/s10468-010-9233-7
- ISSN
- 1386-923X
- eISSN
- 1572-9079
- Language
- English
- Date published
- 02/2012
- Academic Unit
- Mathematics
- Record Identifier
- 9983985705102771
Metrics
22 Record Views