q-invariance of quantum quaternion spheres

2015/10/07 by Saurabh, Bipul
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1510.01862

Abstract

The C^*-algebra of continuous functions on the quantum quaternion sphere H_q²ⁿ can be identified with the quotient algebra C(SP_q(2n)/SP_q(2n-2)). In commutative case i.e. for q=1, the topological space SP(2n)/SP(2n-2) is homeomorphic to the odd dimensional sphere S^4n-1. In this paper, we prove the noncommutative analogue of this result. Using homogeneous C^*-extension theory, we prove that the C^*-algebra C(H_q²ⁿ) is isomorphic to the C^*-algebra C(S_q^4n-1). This further implies that for different values of q ∈ [0,1), the C^*-algebras underlying the noncommutative space H_q²ⁿ are isomorphic.

Related

• On quantum quaternion spheres
• The C^*-algebra of the quantum symplectic sphere
• Spectral dimension of quaternion spheres
• Topological invariance of quantum homogeneous spaces of type B and D
• Isomorphisms of quantum spheres