Vol. 288, No. 2, 2017

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ISSN: 0030-8730
Topological invariance of quantum quaternion spheres

Bipul Saurabh

Vol. 288 (2017), No. 2, 435–452
Abstract

The C-algebra of continuous functions on the quantum quaternion sphere Hq2n can be identified with the quotient algebra C(SPq(2n)SPq(2n 2)). In the commutative case, i.e., for q = 1, the topological space SP(2n)SP(2n 2) is homeomorphic to the odd-dimensional sphere S4n1. In this paper, we prove the noncommutative analogue of this result. Using homogeneous C-extension theory, we prove that the C-algebra C(Hq2n) is isomorphic to the C-algebra C(Sq4n1). This further implies that for different values of q in [0,1), the C-algebras underlying the noncommutative spaces Hq2n are isomorphic.

Keywords
homogeneous extension, quantum double suspension, corona factorization property
Mathematical Subject Classification 2010
Primary: 19K33, 46L80, 58B34
Milestones
Received: 22 June 2016
Revised: 12 December 2016
Accepted: 20 December 2016
Published: 28 April 2017
Authors
Bipul Saurabh
Institute of Mathematical Sciences
CIT Campus, Taramani
Chennai 600113
India