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  An application of the DR-duality theory for compact groups to endomorphism categories of C*-algebras with nontrivial center

Baumgärtel, H., & Lledo, F. (2001). An application of the DR-duality theory for compact groups to endomorphism categories of C*-algebras with nontrivial center. In R. Longo (Ed.), Mathematical physics in mathematics and physics: quantum and operator algebraic aspects (pp. 1-10). Providence, RI: American Mathematical Society.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-55CC-F Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-55CD-D
Genre: Conference Paper

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 Creators:
Baumgärtel, Hellmut, Author
Lledo, Fernando1, Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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 Abstract: In Rev. Math. Phys. 4 (1997) 785 we study Hilbert-C* systems {F,G} where the fixed point algebra A has nontrivial center Z and where A'cap F=Z is satisfied. The corresponding category of all canonical endomorphisms of A contains characteristic mutually isomorphic subcategories of the Doplicher/Roberts-type which are connected with the choice of distinguished G-invariant algebraic Hilbert spaces within the corresponding G-invariant Hilbert Z-modules. We present in this paper the solution of the corresponding inverse problem. More precisely, assuming that the given endomorphism category T of a C*-algebra A with center Z contains a certain subcategory of the DR-type, a Hilbert extension {F,G} of A is constructed such that T is isomorphic to the category of all canonical endomorphisms of A w.r.t. {F,G} and A'cap F=Z. Furthermore, there is a natural equivalence relation between admissible subcategories and it is shown that two admissible subcategories yield A-module isomorphic Hilbert extensions iff they are equivalent. The essential step of the solution is the application of the standard DR-theory to the assigned subcategory.

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Language(s): eng - English
 Dates: 2001
 Publication Status: Issued
 Pages: -
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 Rev. Type: -
 Identifiers: eDoc: 3357
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Title: Conference "Mathematical Physics in Mathematics and Physics, Quantum and Operator Algebraic Aspects
Place of Event: Siena
Start-/End Date: 2000-06-20 - 2000-06-24

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Title: Mathematical physics in mathematics and physics : quantum and operator algebraic aspects
Source Genre: Proceedings
 Creator(s):
Longo, Roberto, Editor
Affiliations:
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Publ. Info: Providence, RI : American Mathematical Society
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 1 - 10 Identifier: -