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Examples of multiparameter CCR flows with non-trivial index

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  27 September 2022

Piyasa Sarkar  and
S. Sundar
Piyasa Sarkar
Affiliation:
Institute of Mathematical Sciences, A CI of Homi Bhabha National Institute, CIT Campus, Taramani, Chennai 600113, India (piyasa10@gmail.com; sundarsobers@gmail.com)
S. Sundar
Affiliation:
Institute of Mathematical Sciences, A CI of Homi Bhabha National Institute, CIT Campus, Taramani, Chennai 600113, India (piyasa10@gmail.com; sundarsobers@gmail.com)
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Abstract

In this paper, we construct uncountably many examples of multiparameter CCR flows, which are not pullbacks of $1$-parameter CCR flows, with any given index. Moreover, the constructed CCR flows are type I in the sense that the associated product system is the smallest subsystem containing its units.

Keywords

E0-semigroupsCCR flowsIndex

MSC classification

Primary: 46L55: Noncommutative dynamical systems
Secondary: 46L99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 3 , August 2022 , pp. 799 - 832
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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