Quantum Orbifolds
Abstract
This is a study of orbifold-quotients of quantum groups (quantum orbifolds $\Theta \rightrightarrows G_q$). These structures have been studied extensively in the case of the quantum $SU_2$ group. I will introduce a generalized mechanism which allows one to construct quantum orbifolds from any compact simple and simply connected quantum group. Associated with a quantum orbifold there is an invariant subalgebra as well as a crossed product algebra. For each spin quantum orbifold, there is a unitary equivalence class of Dirac spectral triples over the invariant subalgebra, and for each effective spin quantum orbifold associated with a finite group action, there is a unitary equivalence class of Dirac spectral triples over the crossed product algebra. As an application I will study a Hopf-equivariant Fredholm index problem.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2014
- DOI:
- 10.48550/arXiv.1412.4589
- arXiv:
- arXiv:1412.4589
- Bibcode:
- 2014arXiv1412.4589H
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematical Physics