Universal enveloping algebras of Leibniz algebras and (co)homology

1993/12/01 by Jean-Louis Loday, Teimuraz Pirashvili · 601 citations
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Biology #Gene #Genetics #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Universal enveloping algebra

paper · doi:10.1007/bf01445099

published in Mathematische Annalen 296(1), 139-158 (Springer Nature)

openalex publication_date 1993/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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• On distributive laws in derived bracket construction and homotopy theory of derived bracket Leibniz algebras
• A New Approach to Defining Cochain Complexes for dual Leibniz algebra
• Combinatorial problems about free groups and algebras
• Polynomial Identities and Codimensions of Two- and Three-Dimensional Metabelian Non-Lie Leibniz Algebras
• (Bi)Hom-Leibniz algebras
• Cohomology and deformation theory of Averaging Leibniz algebras
• Remarks on Leibniz algebras
• Cyclic Leibniz Algebras
• Geometry of Deformations via Incidence Varieties
• Solvable Leibniz algebras with quasi-filiform Lie algebras of maximum length nilradicals
• Nilpotent Sabinin algebras
• Solvable Leibniz algebra with non-Lie and non-split naturally graded filiform nilradical and its rigidity
• A Characteristic Map for Symplectic Manifolds
• On Leibniz algebras, whose subalgebras are either ideals or self-idealizing
• Lie-like Algebras (Superalgeras)
• Biderivations of complete Leibniz algebras
• Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second type L⁴
• Leibniz-dendriform bialgebras and relative Rota-Baxter operators
• Solvable Leibniz algebras with triangular nilradical
• On isomorphism classes and invariants of low dimensional complex filiform Leibniz algebras (part 2)
• The Levi-Civita products of Leibniz algebras with nondegenerate skew-symmetric 2-cocycles
• Derivations in Dialgebras Derivations and Biderivations in Dialgebras
• Universal central extensions of superdialgebras of matrices
• A relative theory of universal central extensions
• Noncommutative renormalization for massless QED
• On classification of complex filiform Leibniz algebras
• A characterization of perfect Leibniz algebras
• Leibniz Homology, Characteristic Classes and K-theory
• Novikov-Jordan algebras
• Derived bracket construction up to homotopy and Schroder numbers
• A counterexample to a Proposition of Feldvoss-Wagemann and Burde-Wagemann
• Some remarks on semisimple Leibniz algebras
• On Description of Isomorphism Classes of filiform Leibniz algebras in dimensions 7 and 8
• Gröbner-Shirshov bases theory and extensions of Leibniz superalgebras
• On exact Courant algebras
• n-Dimensional filiform Leibniz algebras of length (n-1) and their derivations
• Classification of three-dimensional Nijenhuis Leibniz algebras
• Left-right Noncommutative Poisson algebras
• Representations and relative Rota-Baxter operators of Hom-Leibniz Poisson algebras
• The derivations, central extensions and automorphism group of the Lie algebra W
• A natural extension of the universal enveloping algebra functor to crossed modules of Leibniz algebras
• Leibniz 2-algebras, linear 2-racks and the Zamolodchikov Tetrahedron equation
• 3-filiform Leibniz algebras of maximum length
• The structure of restricted Leibniz algebras
• Associative triple trisystems and standard embeddings
• Structure of the extended Schrodinger-Virasoro Lie algebra
• Cohomology of Hom-Leibniz and n-ary Hom-Nambu-Lie superalgebras
• Solvable Leibniz Algebras with Heisenberg Nilradical
• Splitting of operations for alternative and Malcev structures
• H-standard cohomology for Courant-Dorfman algebras and Leibniz algebras
• Derivations and automorphism groups of the original deformative Schrödinger-Virasoro algebras
• An Example of Constructing Versal Deformation for Leibniz Algebras
• On Isomorphism Classes and Invariants of Low Dimensional Complex Filiform Leibniz Algebras (PART 1)
• Lie-isoclinism of pairs of Leibniz algebras
• The Schur Lie-Multiplier of Leibinz Algebras
• Derived bracket construction and anti-cyclic subcomplex of Leibniz (co)homology complex
• Leibniz algebras associated with representations of the Diamond Lie algebra
• Even (Odd) Roots and Simple Leibniz Algebras with Lie Factor sℓ₂
• Polynomial invariants for 3-dimensional Leibniz algebras
• Quadratic n-ary Hom-Nambu algebras
• Leibniz triple systems
• A non-abelian Hom-Leibniz tensor product and applications
• Low-dimensional non-abelian Leibniz cohomology
• A cohomological characterization of Leibniz central extensions of Lie algebras
• A universal enveloping algebra for cocommutative rack bialgebras
• Matrads, biassociahedra, and A_∞-bialgebras
• Deformations of 3-algebras
• Leibniz 2-Algebras and Twisted Courant Algebroids
• Topics on n-ary algebras
• Leibniz algebra deformations of a Lie algebra
• Geometric Rigidity in Moduli Stacks of Algebras
• On (n+1)-Hom-Lie Algebras Induced by n-Hom-Lie Algebras
• Formal symplectic geometry for Leibniz algebras
• 3-Leibniz bialgebras (3-Lie bialgebras)
• On a class of n-Leibniz deformations of the simple Filippov algebras
• Equivariant one-parameter formal deformations of Hom-Leibniz algebras
• Infinitesimal deformations of null-filiform Leibniz superalgebras
• E-Courant Algebroids
• LEIBNIZ SUPERALGEBRAS AND CENTRAL EXTENSIONS
• On the automorphism groups of some Leibniz algebras
• The geometric classification of Leibniz algebras