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PreprintCC BY 4.0arXiv

Crystallization of the quantum Stiefel manifolds SOq(2n+1)/SOq(2n−1)

  • Surajit Biswas
  • Vinay Deshpande
  • Bipul Saurabh
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Abstract

In this paper, we introduce the crystallization C(SO0(2n+1)/SO0(2n−1)) of the C*-algebra C(SOq(2n+1)/SOq(2n−1)). We show that every irreducible representation of C(SO0(2n+1)/SO0(2n−1)) arises as the limit, as q → 0+, of a family of irreducible representations of C(SOq(2n+1)/SOq(2n−1)). As a consequence, we prove that C(SO0(2n+1)/SO0(2n−1)) is the universal C*-algebra generated by a finite set of generators and relations. We then construct a chain of unital essential short exact sequences of C*-algebras, enabling us to compute the K-groups of C(SO0(2n+1)/SO0(2n−1)) and determine explicit generators for them. Using the theory of homogeneous C*-extensions, we prove that C(SO0(2n+1)/SO0(2n−1)) is isomorphic to C(SOq(2n+1)/SOq(2n−1)) for every q ∈ (0,1).

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Cite

BibTeXRIS
BibTeX
@misc{biswas2026crystallization,
  title = {{Crystallization of the quantum Stiefel manifolds $SO_q(2n+1)/SO_q(2n-1)$}},
  author = {Surajit Biswas and Vinay Deshpande and Bipul Saurabh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10377},
  eprint = {2610.10377},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10377},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Crystallization of the quantum Stiefel manifolds SO_q(2n+1)/SO_q(2n−1)
AU  - Surajit Biswas
AU  - Vinay Deshpande
AU  - Bipul Saurabh
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10377
UR  - https://arxiv.org/abs/2610.10377
AB  - In this paper, we introduce the crystallization C(SO_0(2n+1)/SO_0(2n−1)) of the C^*-algebra C(SO_q(2n+1)/SO_q(2n−1)). We show that every irreducible representation of C(SO_0(2n+1)/SO_0(2n−1)) arises as the limit, as q → 0^+, of a family of irreducible representations of C(SO_q(2n+1)/SO_q(2n−1)). As a consequence, we prove that C(SO_0(2n+1)/SO_0(2n−1)) is the universal C^*-algebra generated by a finite set of generators and relations. We then construct a chain of unital essential short exact sequences of C^*-algebras, enabling us to compute the K-groups of C(SO_0(2n+1)/SO_0(2n−1)) and determine explicit generators for them. Using the theory of homogeneous C^*-extensions, we prove that C(SO_0(2n+1)/SO_0(2n−1)) is isomorphic to C(SO_q(2n+1)/SO_q(2n−1)) for every q ∈ (0,1).
ER  -