On the adjoint map of homotopy abelian DG-Lie algebras

Donatella Iacono; Marco Manetti

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Displaying similar documents to “On the adjoint map of homotopy abelian DG-Lie algebras”

Homotopy algebras via resolutions of operads

Markl, Martin

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Summary: All algebraic objects in this note will be considered over a fixed field $k$ of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over $k$ . For standard terminology concerning operads, algebras over operads, etc., see either the original paper by [“The geometry of iterated loop spaces”, Lect. Notes Math. 271 (1972; Zbl 0244.55009)], or an overview [, “La renaissance des opérads”, Sémin. Bourbaki 1994/95, Exp. No....

Deformations of Batalin-Vilkovisky algebras

Olga Kravchenko (2000)

Banach Center Publications

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We show that a graded commutative algebra A with any square zero odd differential operator is a natural generalization of a Batalin-Vilkovisky algebra. While such an operator of order 2 defines a Gerstenhaber (Lie) algebra structure on A, an operator of an order higher than 2 (Koszul-Akman definition) leads to the structure of a strongly homotopy Lie algebra ( $L_{\infty}$ -algebra) on A. This allows us to give a definition of a Batalin-Vilkovisky algebra up to homotopy. We also make a conjecture...

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.

Graded Lie Algebras of depth one.

Rikard Bogvad, Carl Jacobsson (1990)

Manuscripta mathematica

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Homotopy Rinehart cohomology of homotopy Lie-Rinehart pairs.

Kjeseth, Lars (2001)

Homology, Homotopy and Applications

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On the structure of graded transitive Lie algebras.

Post, Gerhard (2002)

Journal of Lie Theory

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Deformation Theory (Lecture Notes)

M. Doubek, Martin Markl, Petr Zima (2007)

Archivum Mathematicum

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First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation between deformations and solutions of the corresponding Maurer-Cartan equation. In Section we generalize the Maurer-Cartan equation to strongly homotopy Lie algebras and prove the homotopy invariance of the moduli space of solutions of this equation....