Morita equivalence problem for symplectic reflection algebras

2024/04/04 by Akaki Tikaradze, Tikaradze, Akaki
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2404.03811

openalex publication_date 2024/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we fully solve the Morita equivalence problem for symplectic reflection algebras associated to direct products of finite subgroups of SL₂(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.

Related

• Morita Equivalence of Cherednik Algebras
• Reflection functors and representations for continuous wreath-product symplectic reflection algebras
• Morita equivalence classes for crossed product of rational rotation algebras
• Gelfand-Kirillov conjecture for symplectic reflection algebras
• Completions of symplectic reflection algebras