Non-associative algebraic structures: classification and structure

Abstract

These are detailed notes for a lecture on "Non-associative Algebraic Structures: Classification and Structure" which I presented as a part of my Agregação em Matemática e Applicações (University of Beira Interior, Covilhã, Portugal, 13-14/03/2023).

References in corpus (70)

• Deformation quantization of Poisson manifolds, I
• Hom-algebras and homology
• Six-dimensional nilpotent Lie algebras
• Classical $\mathbf{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras
• Classification of five-dimensional nilpotent Jordan algebras
• Degenerations of Zinbiel and nilpotent Leibniz algebras
• The algebraic and geometric classification of nilpotent binary Lie algebras
• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
• The algebraic and geometric classification of nilpotent Novikov algebras
• The algebraic and geometric classification of nilpotent anticommutative algebras
• The algebraic and geometric classification of nilpotent bicommutative algebras
• Degenerations of binary Lie and nilpotent Malcev algebras
• Degenerations of Leibniz and anticommutative algebras
• The algebraic and geometric classification of nilpotent terminal algebras
• Non-associative central extensions of null-filiform associative algebras
• Complete classification of algebras of level two
• The classification of $n$-dimensional anticommutative algebras with $(n-3)$-dimensional annihilator
• The classification of $2$-dimensional rigid algebras
• Leibniz Gauge Theories and Infinity Structures
• Transposed Poisson structures on Block Lie algebras and superalgebras
• Poisson Structures on Finitary Incidence Algebras
• Contractions of low-dimensional nilpotent Jordan algebras
• A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations
• Transposed Poisson structures on Witt type algebras
• Infinitesimal deformations of null-filiform Leibniz superalgebras
• Degenerations of Jordan Superalgebras
• Higher Derivations of Finitary Incidence Algebras
• The algebraic and geometric classification of nilpotent noncommutative Jordan algebras
• The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras
• The algebraic classification of nilpotent Tortkara algebras
• Degenerations of Jordan Algebras and ''Marginal'' Algebras
• Transposed Poisson structures on generalized Witt algebras and Block Lie algebras
• Two-Local derivations on associative and Jordan matrix rings over commutative rings
• Conservative algebras of 2-dimensional algebras
• Enhanced Leibniz Algebras: Structure Theorem and Induced Lie 2-Algebra
• Alternative algebras admitting derivations with invertible values and invertible derivations
• On a ternary generalization of Jordan algebras
• Classification of linearly compact simple Nambu-Poisson algebras
• The Freiheitssatz for Generic Poisson Algebras
• The classification of algebras of level two
• Poisson cohomology and quantization
• Some cohomologically rigid solvable Leibniz algebras
• Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras
• Potent preservers of incidence algebras
• The geometric classification of nilpotent algebras
• Transposed Poisson structures on the Lie algebra of upper triangular matrices
• Infinitesimal deformations of naturally graded filiform Leibniz algebras
• Central extensions of 3-dimensional Zinbiel algebras
• The structure of simple noncommutative Jordan superalgebras
• One-generated nilpotent bicommutative algebras
• The algebraic and geometric classification of nilpotent left-symmetric algebras
• Algebras of Jordan brackets and Generalized Poisson algebras
• Modules over linear spaces admitting a multiplicative basis
• $k$-Modules over linear spaces by $n$-linear maps admitting a multiplicative basis
• Split Regular $Hom$-Leibniz Color $3$-Algebras
• Decompositions of linear spaces induced by $n$-linear maps
• The algebraic and geometric classification of nilpotent right alternative algebras
• A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra
• The algebraic and geometric classification of antiassociative algebras
• Classification of algebras of level two in the variety of nilpotent algebras and Leibniz algebras
• The derived non-commutative Poisson bracket on Koszul Calabi-Yau algebras
• Deformation quantization of Leibniz algebras
• One-generated nilpotent assosymmetric algebras
• The algebraic classification of nilpotent commutative algebras
• Classification of the four-dimensional power-commutative real division algebras
• Abelian groups gradings on null-filiform and one-parametric filiform Leibniz algebras
• Periodic derivations and prederivations of Lie algebras
• Lie maps on alternative rings preserving idempotents
• Assosymmetric algebras under jordan product
• The geometric classification of $2$-step nilpotent algebras and applications

Cited by in corpus (6)

• Transposed Poisson structures on the Lie algebra of upper triangular matrices
• Transposed Poisson structures on Lie incidence algebras
• Graded anti-pre-Lie algebraic structures on Witt and Virasoro algebras
• The algebraic and geometric classification of right alternative and semi-alternative algebras
• The algebraic and geometric classification of derived Jordan and bicommutative algebras
• Quantizations of transposed Poisson algebras by Novikov deformations