Work

Co-universal algebras associated to product systems, and gauge-invariant uniqueness theorems

Year: 2011

Type: article

Abstract: Let (G, P) be a quasi-lattice ordered group, and let X be a product system over P of Hilbert bimodules. Under mild hypotheses, we associate to X a C*-algebra which is co-universal for injective Nica covariant Toeplitz representations of X which preserve the gauge coaction. Under appropriate amenability criteria, this co-universal C*-algebra coincides with the Cuntz-Nica-Pimsner algebra introduced by Sims and Yeend. We prove two key uniqueness theorems, and indicate how to use our theorems to realize a number of reduced crossed products as instances of our co-universal algebras. In each case, it is an easy corollary that the Cuntz-Nica-Pimsner algebra is isomorphic to the corresponding full crossed product.

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms/pdq028

Authors: Toke M. Carlsen, Nadia S. Larsen, Aidan Sims, Sean T. Vittadello

Institutions: Norwegian University of Science and Technology, University of Oslo, University of Wollongong

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Norges Forskningsråd

OpenAlex ID: W2008341820

FWCI: 1.349

Cites: 1

Cited by: 46

Related to: 9