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Index Semigroup and Indexing on von Neumann Algebras

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Abstract

In this paper, we study a semigroup induced by the index morphism on finite trees. This index morphism classify the set of all finite trees under certain equivalence relation, and this classification forms a semigroup. We define the indexing α by a map from this semigroup into the family of all von Neumann algebras. Then the images of α become new von Neumann algebras containing their natural diagonal W*-subalgebras. For naturally determined conditional expectations with affiliation, the Watatani’s extended Jones index of each image of α is preserved by the elements of the semigroup.

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Authors and Affiliations

  1. Department of Mathematics, St. Ambrose University, 518 W. Locust st., Davenport, IA, 52803, USA

    Ilwoo Cho

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  1. Ilwoo Cho
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Correspondence to Ilwoo Cho.

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Communicated by Palle Jorgensen.

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Cho, I. Index Semigroup and Indexing on von Neumann Algebras. Complex Anal. Oper. Theory 8, 683–707 (2014). https://doi.org/10.1007/s11785-011-0208-4

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  • DOI: https://doi.org/10.1007/s11785-011-0208-4

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