Displaying similar documents to “Deformations of Batalin-Vilkovisky 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....

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....

Examples of homotopy Lie algebras

Klaus Bering, Tom Lada (2009)

Archivum Mathematicum

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We look at two examples of homotopy Lie algebras (also known as L ∞ algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators Δ to verify the homotopy Lie data is shown to produce the same results.

From Poisson algebras to Gerstenhaber algebras

Yvette Kosmann-Schwarzbach (1996)

Annales de l'institut Fourier

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Constructing an even Poisson algebra from a Gerstenhaber algebra by means of an odd derivation of square 0 is shown to be possible in the category of Loday algebras (algebras with a non-skew-symmetric bracket, generalizing the Lie algebras, heretofore called Leibniz algebras in the literature). Such “derived brackets” give rise to Lie brackets on certain quotient spaces, and also on certain Abelian subalgebras. The construction of these derived brackets explains the origin of the Lie...