Graded Lie Algebras of depth one.

Rikard Bogvad; Carl Jacobsson

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A correspondence between finite-dimensional Lie superalgebras and supergroups.

Vladimir G. Pestov (1992)

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On the structure of graded transitive Lie algebras.

Post, Gerhard (2002)

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Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras

Johannes Huebschmann (2000)

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Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms of certain associated differential (bi)graded Lie and G(erstenhaber)-algebras; in particular the G-algebra arising from an almost complex structure is a (strict) d(ifferential)...

Graded Lie algebras with classical reductive null component.

Georgia Benkart, Thomas Gregory (1989)

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Contact Lie algebras of vector fields on the plane.

Doubrov, Boris M., Komrakov, Boris P. (1999)

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Homotopy Lie algebras and fundamental groups via deformation theory

Martin Markl, Stefan Papadima (1992)

Annales de l'institut Fourier

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We formulate first results of our larger project based on first fixing some easily accessible invariants of topological spaces (typically the cup product structure in low dimensions) and then studying the variations of more complex invariants such as $π_{*} Ω S$ (the homotopy Lie algebra) or ${gr}^{*} π_{1} S$ (the graded Lie algebra associated to the lower central series of the fundamental group). We prove basic rigidity results and give also an application in low-dimensional topology.

On the adjoint map of homotopy abelian DG-Lie algebras

Donatella Iacono, Marco Manetti (2019)

Archivum Mathematicum

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We prove that a differential graded Lie algebra is homotopy abelian if its adjoint map into its cochain complex of derivations is trivial in cohomology. The converse is true for cofibrant algebras and false in general.