Morita equivalence problem for symplectic reflection algebras
Abstract
In this paper we fully solve the Morita equivalence problem for symplectic reflection algebras associated to direct products of finite subgroups of $SL_2(\mathbb{C})$. Namely, given a pair of such symplectic reflection algebras $H_c, H_{c'}$,then $H_c$ is Morita equivalent to $H_c'$ if and only if they are related by a standard Morita equivalence. We also establish new cases for Morita classification problem for type A rational Cherednik algebras. Our approach crucially relies on the reduction modulo large primes.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2024
- DOI:
- 10.48550/arXiv.2404.03811
- arXiv:
- arXiv:2404.03811
- Bibcode:
- 2024arXiv240403811T
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Quantum Algebra
- E-Print:
- 14 pages, preliminary version, all comments welcome