Deformations of nilpotent groups and homotopy symmetric C*-algebras

Dadarlat, Marius and Pennig, Ulrich ORCID: https://orcid.org/0000-0001-5441-6130 2017. Deformations of nilpotent groups and homotopy symmetric C*-algebras. Mathematische Annalen 367 , pp. 121-134. 10.1007/s00208-016-1379-0

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Abstract

The homotopy symmetric C*-algebras are those separable C*-algebras for which one can unsuspend in E-theory. We find a new simple condition that characterizes homotopy symmetric nuclear C*-algebras and use it to show that the property of being homotopy symmetric passes to nuclear C*-subalgebras and it has a number of other significant permanence properties. As an application, we show that if I(G) is the kernel of the trivial representation for a countable discrete torsion free nilpotent group G, then I(G) is homotopy symmetric and hence the Kasparov group KK(I(G), B) can be realized as the homotopy classes of asymptotic morphisms [[I(G),B⊗K]] for any separable C*-algebra B.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer
ISSN:	0025-5831
Date of First Compliant Deposit:	2 December 2016
Last Modified:	17 Nov 2024 11:30
URI:	https://orca.cardiff.ac.uk/id/eprint/89462

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