Non-associative structures of commutative algebras related with quadratic Poisson brackets

DOI10.1007/s40879-020-00398-wzbMath1457.16019OpenAlexW3004589026MaRDI QIDQ1987710

Orest D. Artemovych, D. L. Blackmore, Anatoliy K. Prykarpatsky

Publication date: 15 April 2020

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40879-020-00398-w

zbMATH Keywords

Lie-Poisson structureBalinsky-Novikov algebrapre-Poisson bracketslocal quadratic Poisson structures

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Invariance and symmetry properties for PDEs on manifolds (58J70) Initial value problems for nonlinear higher-order PDEs (35G25) Derivations and commutative rings (13N15) Geometric theory, characteristics, transformations in context of PDEs (35A30) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Related Items (1)

The algebraic and geometric classification of Zinbiel algebras

Cites Work

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• A simple way of making a Hamiltonian system into a bi-Hamiltonian one
• What is a classical r-matrix?
• Novikov algebras and Novikov structures on Lie algebras
• The Lie structure of a commutative ring with a derivation
• Complete left-invariant affine structures on nilpotent Lie groups
• On simple Novikov algebras and their irreducible modules
• Hamiltonian operators and algebraic structures related to them
• Chronological algebras and nonstationary vector fields
• Universal enveloping algebras of Leibniz algebras and (co)homology
• Novikov-Poisson algebras
• Nilpotency of Zinbiel algebras
• A class of simple nonassociative algebras
• Quadratic Poisson brackets and the Drinfeld theory for associative algebras
• The classification of Novikov algebras in low dimensions
• On the realization of transitive Novikov algebras
• The classification of Novikov algebras in low dimensions: invariant bilinear forms
• Differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann hierarchy revisited
• Novikov Algebras and a Classification of Multicomponent Camassa-Holm Equations
• Novikov-Poisson algebras and associative commutative derivation algebras
• ZINBIEL ALGEBRAS AND COMMUTATIVE ALGEBRAS WITH DIVIDED POWERS
• THE EXPONENTIAL REPRESENTATION OF FLOWS AND THE CHRONOLOGICAL CALCULUS
• Lie Rings of Derivations of Associative Rings
• The Lie Structure of a Commutative Ring with a Derivation
• On the algebraic structures connected with the linear Poisson brackets of hydrodynamics type
• On computation of the logarithm of the Chen-Fliess series for nonlinear systems
• Quadratic Poisson brackets compatible with an algebra structure
• CUP-Product for Leibnitz Cohomology and Dual Leibniz Algebras.
• Dialgebras and related operads
• Transitive Novikov algebras on four-dimensional nilpotent Lie algebras
• Classification of simple Novikov algebras and their irreducible modules of characteristic 0
• Solutions of the classical Yang-Baxter equation for simple Lie algebras

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