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Cohomology and deformations of dendriform algebras, and Dend∞-algebras
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A dendriform algebra is an associative algebra whose product splits into two binary operations and the associativity splits into three new identities as mentioned in this paper, where the product can be expressed as a binary operation.Abstract:
A dendriform algebra is an associative algebra whose product splits into two binary operations and the associativity splits into three new identities. These algebras arise naturally from some combi...read more
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Deformations of associative Rota-Baxter operators
TL;DR: In this paper, an explicit graded Lie algebra whose Maurer-Cartan elements are given by O -operators is constructed. And the cohomology for an O -operator can also be seen as the Hochschild cohomorphology of a certain algebra with coefficients in a suitable bimodule.
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The L∞-deformations of associative Rota–Baxter algebras and homotopy Rota–Baxter operators
TL;DR: In this paper, an L∞[1]-algebra whose Maurer-Cartan elements are precisely relative Rota-Baxter algebras is constructed using Voronov derived bracket and a recent work of Lazarev, Sheng, and Tang.
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Deformations of Loday-type algebras and their morphisms
TL;DR: In this article, formal deformation of multiplication in an operad is studied, which closely resembles Gerstenhaber's deformation theory for associative algebras and their twisted analogs.
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Involutive and oriented dendriform algebras
Apurba Das,Ripan Saha +1 more
TL;DR: In this paper, a cohomology theory for oriented dendriform algebras is developed, which is closely related to extensions and governs the simultaneous deformations of dendriniform structures and the orientation.
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Twisted Rota-Baxter families and NS-family algebras
TL;DR: In this article , a notion of twisted Rota-Baxter family and its relation with (tri)dendriform family algebras have been discovered. But the concept of twisted O-operator family is not defined in this paper.
References
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Journal ArticleDOI
On the Deformation of Rings and Algebras
TL;DR: In this article, the deformation theory for algebras is studied in terms of the set of structure constants as a parameter space, and an example justifying the choice of parameter space is given.
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Introduction to SH Lie algebras for physicists
Tom Lada,Jim Stasheff +1 more
TL;DR: In this paper, Stasheff et al. introduced the Lie algebra of closed string theory and proved that the full Fock complex of the theory is a Lie algebra, with the BRST difierential Q.
Journal ArticleDOI
Koszul duality for operads
Victor Ginzburg,Mikhail Kapranov +1 more
TL;DR: In this paper, the authors introduce a class of operads called quadratic, and introduce a distinguished subclass of Koszul operads, which can be interpreted as the Verdier duality functor on sheaves.
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Strongly homotopy Lie algebras
Tom Lada,Martin Markl +1 more
TL;DR: In this paper, Strongly homotopy lie algebras have been studied in the context of algebraic graph theory, and they are shown to be strongly homotopomorphic.