Degenerations of Poisson algebras

DOI10.1142/S0219498825500872MaRDI QIDQ6669425

Candido Martín González, Hani Abdelwahab, Amir Fernández Ouaridi

Publication date: 22 January 2025

Published in: Journal of Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

degenerationPoisson algebrasalgebraic classificationgeometric classification

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Fibrations, degenerations in algebraic geometry (14D06) Solvable, nilpotent (super)algebras (17B30) Nonassociative algebras satisfying other identities (17A30) Other nonassociative rings and algebras (17D99) Ternary compositions (17A40)

Cites Work

• Poisson algebras in terms of non-associative algebras
• Poisson structures on \(\mathbb C[X_1,\dots,X_n]\) associated with rigid Lie algebras
• \(n\)-Lie algebras
• Varieties of nilpotent Lie algebras of dimension less than six
• A characterization of orbit closure and applications
• Classification of orbit closures of 4-dimensional complex Lie algebras
• On foundation of the generalized Nambu mechanics
• The algebraic classification and degenerations of nilpotent Poisson algebras
• Degenerations of nilpotent algebras
• Degenerations of Jordan superalgebras
• Some classes of nilpotent associative algebras
• The algebraic and geometric classification of nilpotent Lie triple systems up to dimension four
• Degenerations of 6-dimensional nilpotent lie algebras over C
• Degenerations of pre-Lie algebras
• Symplectic geometry
• The geometric classification of Leibniz algebras
• The classification of N-dimensional non-associative Jordan algebras with (N − 3)-dimensional annihilator
• Generalized Hamiltonian Dynamics
• Degenerations of Jordan Algebras and “Marginal” Algebras
• The classification of 2-dimensional rigid algebras
• The Variety of Two-dimensional Algebras Over an Algebraically Closed Field
• Degenerations of Leibniz and Anticommutative Algebras
• CLASSIFICATION OF ORBIT CLOSURES IN THE VARIETY OF THREE-DIMENSIONAL NOVIKOV ALGEBRAS
• Central extensions of filiform associative algebras
• Jacobi and Poisson algebras

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