-structure on the Cohomology of the Free 2-Nilpotent Lie Algebra
Michel Dubois-Violette, Todor Popov (2013)
Publications de l'Institut Mathématique
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Michel Dubois-Violette, Todor Popov (2013)
Publications de l'Institut Mathématique
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Kjeseth, Lars (2001)
Homology, Homotopy and Applications
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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....
Markl, Martin
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Summary: All algebraic objects in this note will be considered over a fixed field of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over . 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....
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 (-algebra) on A. This allows us to give a definition of a Batalin-Vilkovisky algebra up to homotopy. We also make a conjecture...