Deformations et rigidite geometrique des algebres de leibniz

DOI10.1080/00927879608825618zbMath0855.17021OpenAlexW2021061002MaRDI QIDQ4874754

David Balavoine

Publication date: 10 June 1996

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879608825618

zbMATH Keywords

cohomologyalgebraic varietiesadjoint representationLeibniz algebraformal deformation2-cocycle

Mathematics Subject Classification ID

Homological methods in Lie (super)algebras (17B55) Cohomology of Lie (super)algebras (17B56) Formal methods and deformations in algebraic geometry (14D15)

Related Items (21)

Deformation of Dual Leibniz Algebra Morphisms ⋮ Corrigendum to: ``Classification of solvable Leibniz algebras with naturally graded filiform nilradical. ⋮ On the degenerations of solvable Leibniz algebras ⋮ Some irreducible components of the variety of complex \((n + 1)\)-dimensional Leibniz algebras ⋮ A rigid Leibniz algebra with non-trivial \(HL^2\) ⋮ Leibniz algebras associated with representations of Euclidean Lie algebra ⋮ Infinitesimal deformations of null-filiform Leibniz superalgebras ⋮ Solvable Leibniz algebras with \(NF_n\bigoplus F_m^1\) nilradical ⋮ Cohomologically rigid solvable Leibniz algebras with nilradical of arbitrary characteristic sequence ⋮ Some cohomologically rigid solvable Leibniz algebras ⋮ On the cohomology of solvable Leibniz algebras ⋮ Solvable Leibniz algebras with quasi-filiform Lie algebras of maximum length nilradicals ⋮ On Leibniz cohomology ⋮ Semisimple Leibniz algebras, their derivations and automorphisms ⋮ The second cohomology group of simple Leibniz algebras ⋮ Infinitesimal deformations of naturally graded filiform Leibniz algebras ⋮ Leibniz algebras associated with representations of the diamond Lie algebra ⋮ Coalgebraic approach to the Loday infinity category, stem differential for \(2n\)-ary graded and homotopy algebras ⋮ Solvable Leibniz algebras with naturally graded non-Liep-filiform nilradicals ⋮ The classification of filiform Leibniz superalgebras of nilindex \(n+m\) ⋮ Classification of (2n−1)-dimensional solvable Leibniz algebras with n-dimensional nilradical

Cites Work

• An introduction to algebraic deformation theory
• The construction of cofree coalgebras
• Coalgebras over a commutative ring
• Universal enveloping algebras of Leibniz algebras and (co)homology
• Commutative algebra cohology and deformations of Lie and associative algebras
• Effacement et déformation
• On the deformation of rings and algebras

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