Chakraborty, Partha Sarathi ; Pal, Arupkumar (2007) Torus Equivariant Spectral Triples for Odd-Dimensional Quantum Spheres Coming from C *-Extensions Letters in Mathematical Physics, 80 (1). pp. 57-68. ISSN 0377-9017
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Official URL: http://doi.org/10.1007/s11005-007-0149-z
Related URL: http://dx.doi.org/10.1007/s11005-007-0149-z
Abstract
The torus group (S 1)ℓ+1 has a canonical action on the odd-dimensional sphere S 2ℓ+1 q . We take the natural Hilbert space representation where this action is implemented and characterize all odd spectral triples acting on that space and equivariant with respect to that action. This characterization gives a construction of an optimum family of equivariant spectral triples having nontrivial K-homology class thus generalizing our earlier results for SU q (2). We also relate the triple we construct with the C *-extension 0⟶K⊗C(S1)⟶C(S2ℓ+3q)⟶C(S2ℓ+1q)⟶0.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer Nature Switzerland AG. |
| Keywords: | Spectral Triples; Noncommutative Geometry; Quantum Group. |
| ID Code: | 116915 |
| Deposited On: | 08 Apr 2021 07:18 |
| Last Modified: | 08 Apr 2021 07:18 |
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