The algebraic and geometric classification of compatible pre-Lie algebras

DOI10.3842/sigma.2024.107MaRDI QIDQ6657484

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Publication date: 6 January 2025

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

zbMATH Keywords

algebraic classificationgeometric classificationcompatible associative algebracompatible pre-Lie algebracompatible algebra

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Nonassociative algebras satisfying other identities (17A30) Lie-admissible algebras (17D25)

Cites Work

• On the free Lie algebra with multiple brackets
• Pairs of compatible associative algebras, classical Yang-Baxter equation and quiver representations
• Operads of compatible structures and weighted partitions
• Compatible associative products and trees
• Compatible Lie brackets and the Yang-Baxter equation
• Varieties of nilpotent Lie algebras of dimension less than six
• Compatible Lie brackets and integrable equations of the principal chiral model type
• On the passage from finite braces to pre-Lie rings
• The algebraic classification and degenerations of nilpotent Poisson algebras
• \(F\)-manifold algebras and deformation quantization via pre-Lie algebras
• Combinatorial bases for multilinear parts of free algebras with two compatible brackets
• Left-symmetric algebras, or pre-Lie algebras in geometry and physics
• Compatible \(L_\infty \)-algebras
• Polynomial identities in Novikov algebras
• Pre-Lie algebras and the rooted trees operad
• Integrable matrix equations related to pairs of compatible associative algebras
• Algebraic structures connected with pairs of compatible associative algebras
• Compatible Lie brackets related to elliptic curve
• Degenerations of pre-Lie algebras
• The Variety of Two-dimensional Algebras Over an Algebraically Closed Field
• CLASSIFICATION OF ORBIT CLOSURES IN THE VARIETY OF THREE-DIMENSIONAL NOVIKOV ALGEBRAS
• L ∞ -structures and cohomology theory of compatible O-operators and compatible dendriform algebras
• Maurer-Cartan characterizations and cohomologies of compatible Lie algebras
• The geometric classification of nilpotent algebras
• Cohomology and deformations of compatible Hom-Lie algebras
• Compatible structures of nonsymmetric operads, Manin products and Koszul duality
• (Co)homology of compatible associative algebras
• From braces to pre-Lie rings
• Deformations, cohomologies and abelian extensions of compatible 3-Lie algebras
• Computing subalgebras and \(\mathbb{Z}_2\)-gradings of simple Lie algebras over finite fields
• On classification and deformations of Lie-Rinehart superalgebras
• Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras
• Cohomology and deformations of left-symmetric Rinehart algebras
• Non-associative algebraic structures: classification and structure
• Noncommutative algebra and representation theory: symmetry, structure \& invariants

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