Reduced Pre-Lie Algebraic Structures, the Weak and Weakly Deformed Balinsky–Novikov Type Symmetry Algebras and Related Hamiltonian Operators

Reduced Pre-Lie Algebraic Structures, the Weak and Weakly Deformed Balinsky–Novikov Type Symmetry Algebras and Related Hamiltonian Operators

The Lie algebraic scheme for constructing Hamiltonian operators is differential-algebraically recast and an effective approach is devised for classifying the underlying algebraic structures of integrable Hamiltonian systems. Lie⁻Poisson analysis on the adjoint space to toroidal loop Lie al...

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Bibliographic Details
Main Authors: Orest D. Artemovych, Alexander A. Balinsky, Denis Blackmore, Anatolij K. Prykarpatski
Format: Article
Language:English
Published: MDPI AG 2018-11-01
Series:Symmetry
Subjects:
nonassociative algebra
loop algebra
Lie–Poisson structure
Hamiltonian operator
R-structure
toroidal loop algebra
Poisson structure
Hamiltonian system
derivation
Balinsky– Novikov algebra
weak Balinsky–Novikov algebra
weakly deformed Balinsky–Novikov algebra
reduced pre-Lie algebra
fermionic Balinsky–Novikov algebra
Lie algebra
Lie derivation
Leibniz algebra
Riemann algebra
Online Access:https://www.mdpi.com/2073-8994/10/11/601

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