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On the Wiener-Hopf compactification of a symmetric cone


Author: S. Sundar
Journal: Proc. Amer. Math. Soc. 145 (2017), 1141-1151
MSC (2010): Primary 46L80; Secondary 17CXX
DOI: https://doi.org/10.1090/proc/13317
Published electronically: September 8, 2016
MathSciNet review: 3589314
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Abstract: Let $ V$ be a finite dimensional real Euclidean Jordan algebra with the identity element $ 1$. Let $ Q$ be the closed convex cone of squares. We show that the Wiener-Hopf compactification of $ Q$ is the interval $ \{x \in V: -1 \leq x \leq 1\}$. As a consequence, we deduce that the $ K$-groups of the Wiener-Hopf $ C^{*}$-algebra associated to $ Q$ are trivial.


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Additional Information

S. Sundar
Affiliation: Chennai Mathematical Institute, H1 Sipcot IT Park, Siruseri, Padur, 603103, Tamilnadu, India
Email: sundarsobers@gmail.com

DOI: https://doi.org/10.1090/proc/13317
Keywords: Wiener-Hopf $C^{*}$-algebras, compactification, Jordan algebras
Received by editor(s): February 2, 2016
Received by editor(s) in revised form: May 3, 2016
Published electronically: September 8, 2016
Communicated by: Adrian Ioana
Article copyright: © Copyright 2016 American Mathematical Society