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Relevant bibliographies by topics / Gerstenhaber algebra

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Journal articles

Academic literature on the topic 'Gerstenhaber algebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Gerstenhaber algebra"

1

Volkov, Yury. "Gerstenhaber Bracket on the Hochschild Cohomology via An Arbitrary Resolution." Proceedings of the Edinburgh Mathematical Society 62, no. 3 (2019): 817–36. http://dx.doi.org/10.1017/s0013091518000901.

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AbstractWe prove formulas of different types that allow us to calculate the Gerstenhaber bracket on the Hochschild cohomology of an algebra using some arbitrary projective bimodule resolution for it. Using one of these formulas, we give a new short proof of the derived invariance of the Gerstenhaber algebra structure on Hochschild cohomology. We also give some new formulas for the Connes differential on the Hochschild homology that lead to formulas for the Batalin–Vilkovisky (BV) differential on the Hochschild cohomology in the case of symmetric algebras. Finally, we use one of the obtained formulas to provide a full description of the BV structure and, correspondingly, the Gerstenhaber algebra structure on the Hochschild cohomology of a class of symmetric algebras.

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2

Lyu, Weiguo, and Yuling Wu. "The Hochschild Cohomology Ring of Temperley–Lieb Algebras Revisited." Algebra Colloquium 27, no. 04 (2020): 669–86. http://dx.doi.org/10.1142/s1005386720000565.

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3

Yu, Xuan. "Operad with a prescribed element." Journal of Algebra and Its Applications 17, no. 09 (2018): 1850174. http://dx.doi.org/10.1142/s0219498818501748.

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We study operad with a prescribed element (of its underlying degree one component), generalize some of the classical results of Gerstenhaber and Voronov [M. Gerstenhaber and A. A. Voronov, Homotopy G-algebras and moduli space operad, Int. Math. Res. Not. 3 (1995) 141–153]. In particular, we introduce and show that Hom–Loday algebra cohomologies carry such structures when the Hom-structure twist is an idempotent.

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4

MICHÉA, SÉBASTIEN, and GLEB NOVITCHKOV. "BV-GENERATORS AND LIE ALGEBROIDS." International Journal of Mathematics 16, no. 10 (2005): 1175–91. http://dx.doi.org/10.1142/s0129167x05003247.

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Let [Formula: see text] be a Gerstenhaber algebra generated by [Formula: see text] and [Formula: see text]. Given a degree -1 operator D on [Formula: see text], we find the condition on D that makes [Formula: see text] a BV-algebra. Subsequently, we apply it to the Gerstenhaber or BV algebra associated to a Lie algebroid and obtain a global proof of the correspondence between BV-generators and flat connections.

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5

GOZE, MICHEL, and ELISABETH REMM. "VALUED DEFORMATIONS OF ALGEBRAS." Journal of Algebra and Its Applications 03, no. 04 (2004): 345–65. http://dx.doi.org/10.1142/s0219498804000915.

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We develop a notion of deformations using a valuation ring as a ring of coefficients. This allows us in particular to consider the classical Gerstenhaber deformations of associative or Lie algebras as valued deformations and to solve the equation of deformations in a polynomial framework. We consider also deformations of the enveloping algebra of a rigid Lie algebra and we define valued deformations for some classes of non associative algebras.

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6

Shroff, Piyush, and Sarah Witherspoon. "PBW deformations of quantum symmetric algebras and their group extensions." Journal of Algebra and Its Applications 15, no. 03 (2016): 1650049. http://dx.doi.org/10.1142/s0219498816500493.

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We examine PBW deformations of finite group extensions of quantum symmetric algebras, in particular the quantum Drinfeld orbifold algebras defined by the first author. We give a homological interpretation, in terms of Gerstenhaber brackets, of the necessary and sufficient conditions on parameter functions to define a quantum Drinfeld orbifold algebra, thus clarifying the conditions. In case the acting group is trivial, we determine conditions under which such a PBW deformation is a generalized enveloping algebra of a color Lie algebra; our PBW deformations include these algebras as a special case.

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7

Schechtman, Vadim. "De Rham Complex of a Gerstenhaber Algebra." Moscow Mathematical Journal 15, no. 4 (2015): 817–32. http://dx.doi.org/10.17323/1609-4514-2015-15-4-817-832.

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8

Arenas, Manuel, Irvin Roy Hentzel, and Alicia Labra. "Commutative non-power-associative algebras." International Journal of Algebra and Computation 29, no. 08 (2019): 1527–39. http://dx.doi.org/10.1142/s0218196719500619.

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We study commutative algebras satisfying the identity [Formula: see text] It is known that for [Formula: see text] and for characteristic not [Formula: see text] or [Formula: see text], the algebra is a commutative power-associative algebra. These algebras have been widely studied by Albert, Gerstenhaber and Schafer. For [Formula: see text] Guzzo and Behn in 2014 proved that commutative algebras of dimension [Formula: see text] satisfying [Formula: see text] are solvable. We consider the remaining values of [Formula: see text] We prove that commutative algebras satisfying [Formula: see text] with [Formula: see text] and generated by one element are nilpotent of nilindex [Formula: see text] (we assume characteristic of the field [Formula: see text]).

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9

Ionescu, Lucian M. "Nonassociative Algebras: A Framework for Differential Geometry." International Journal of Mathematics and Mathematical Sciences 2003, no. 60 (2003): 3777–95. http://dx.doi.org/10.1155/s0161171203303023.

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A nonassociative algebra endowed with a Lie bracket, called atorsion algebra, is viewed as an algebraic analog of a manifold with an affine connection. Its elements are interpreted as vector fields and its multiplication is interpreted as a connection. This provides a framework for differential geometry on a formal manifold with a formal connection. A torsion algebra is a natural generalization of pre-Lie algebras which appear as the torsionless case. The starting point is the observation that the associator of a nonassociative algebra is essentially the curvature of the corresponding Hochschild quasicomplex. It is a cocycle, and the corresponding equation is interpreted as Bianchi identity. The curvature-associator-monoidal structure relationships are discussed. Conditions on torsion algebras allowing to construct an algebra of functions, whose algebra of derivations is the initial Lie algebra, are considered. The main example of a torsion algebra is provided by the pre-Lie algebra of Hochschild cochains of aK-module, with Lie bracket induced by Gerstenhaber composition.

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10

Kadeishvili, T. "B ∞-Algebra Structure in Homology of a Homotopy Gerstenhaber Algebra." Journal of Mathematical Sciences 218, no. 6 (2016): 778–87. http://dx.doi.org/10.1007/s10958-016-3064-y.

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