{
  "id": "2404.03811",
  "version": "v1",
  "published": "2024-04-04T21:31:23.000Z",
  "updated": "2024-04-04T21:31:23.000Z",
  "title": "Morita equivalence problem for symplectic reflection algebras",
  "authors": [
    "Akaki Tikaradze"
  ],
  "comment": "14 pages, preliminary version, all comments welcome",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-04T21:31:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symplectic reflection algebras",
      "morita equivalence problem",
      "reduction modulo large primes",
      "standard morita equivalence",
      "rational cherednik algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}