Commutative Poisson algebras from deformations of noncommutative algebras

DOI10.1007/S11005-024-01855-3MaRDI QIDQ6622491

Alexander V. Mikhailov, Pol Vanhaecke

Publication date: 22 October 2024

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Poisson algebrasdeformation quantisationPoisson modulesHamiltonian derivationsdeformations of noncommutative algebrasHeisenberg derivations

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Applications of Lie algebras and superalgebras to integrable systems (17B80) Deformation quantization, star products (53D55) Poisson algebras (17B63) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)

Cites Work

• Title not available (Why is that?)
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• On integrability of the Kontsevich non-Abelian ODE system
• Noncommutative geometry and quiver algebras
• Deformation theory and quantization. I: Deformations of symplectic structures
• Deformation theory and quantization. II: Physical applications
• Semiquantum geometry
• Ring theory from symplectic geometry
• The fundamental equations of quantum mechanics.
• Integrable ODEs on associative algebras
• Quantisations of the Volterra hierarchy
• Double Poisson vertex algebras and non-commutative Hamiltonian equations
• Double Poisson algebras
• Quantisation ideals of nonabelian integrable systems
• Hamiltonians for the quantised Volterra hierarchy

Related Items (1)

Hamiltonians for the quantised Volterra hierarchy

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