Finite dimensional Hopf actions on deformation quantizations

2016/02/01 by Pavel Etingof, Etingof, Pavel, Chelsea Walton +1 · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1602.00532

openalex publication_date 2016/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study when a finite dimensional Hopf action on a quantum formal deformation A of a commutative domain A₀ (i.e., a deformation quantization) must factor through a group algebra. In particular, we show that this occurs when the Poisson center of the fraction field of A₀ is trivial.

Cited by

• On the classification of quantum symmetries
• Hopf actions on Poisson algebras

Related

• Hopf actions on Poisson algebras
• Universal Deformation Formula, Formality and Actions
• Topological Hopf algebras, quantum groups and deformation quantization
• Finite dimensional Hopf actions on Weyl algebras
• Group Actions in Deformation Quantisation