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:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.03811
 arXiv:
 arXiv:2404.03811
 Bibcode:
 2024arXiv240403811T
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Quantum Algebra
 EPrint:
 14 pages, preliminary version, all comments welcome