Displaying similar documents to “Lie bialgebras real cohomology.”

The local integration of Leibniz algebras

Simon Covez (2013)

Annales de l’institut Fourier

Similarity:

This article gives a local answer to the coquecigrue problem for Leibniz algebras, that is, the problem of finding a generalization of the (Lie) group structure such that Leibniz algebras are the corresponding tangent algebra structure. Using links between Leibniz algebra cohomology and Lie rack cohomology, we generalize the integration of a Lie algebra into a Lie group by proving that every Leibniz algebra is isomorphic to the tangent Leibniz algebra of a local Lie rack. This article...

Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras

Junxia Zhu, Liangyun Chen (2021)

Czechoslovak Mathematical Journal

Similarity:

We study Hom-Lie superalgebras of Heisenberg type. For 3-dimensional Heisenberg Hom-Lie superalgebras we describe their Hom-Lie super structures, compute the cohomology spaces and characterize their infinitesimal deformations.

Deformations of Lie brackets: cohomological aspects

Marius Crainic, Ieke Moerdijk (2008)

Journal of the European Mathematical Society

Similarity:

We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which “controls” deformations of the structure bracket of the algebroid.

An extention of Nomizu’s Theorem –A user’s guide–

Hisashi Kasuya (2016)

Complex Manifolds

Similarity:

For a simply connected solvable Lie group G with a lattice Γ, the author constructed an explicit finite-dimensional differential graded algebra A*Γ which computes the complex valued de Rham cohomology H*(Γ, C) of the solvmanifold Γ. In this note, we give a quick introduction to the construction of such A*Γ including a simple proof of H*(A*Γ) ≅ H*(Γ, C).

Leibniz cohomology for differentiable manifolds

Jerry M. Lodder (1998)

Annales de l'institut Fourier

Similarity:

We propose a definition of Leibniz cohomology, H L * , for differentiable manifolds. Then H L * becomes a non-commutative version of Gelfand-Fuks cohomology. The calculations of H L * ( R n ; R ) reduce to those of formal vector fields, and can be identified with certain invariants of foliations.