Results 11 to 20 of about 2,546 (128)
Commutators of Pre-Lie n-Algebras and PL∞-Algebras
Mathematics, 2021 We show that a PL∞-algebra V can be described by a nilpotent coderivation of degree −1 on coalgebra P*V. Based on this result, we can generalise the result of Lada to show that every A∞-algebra carries a PL∞-algebra structure and every PL∞-algebra ...
Mengjun Wang, Zhixiang Wu
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Nijenhuis Operators on 2D Pre-Lie Algebras and 3D Associative Algebras
AxiomsIn this paper, we describe all Nijenhuis operators on 2-dimensional complex pre-Lie algebras and 3-dimensional complex associative algebras. As an application, using these operators, we obtain solutions to the classical Yang-Baxter equation on the ...
Xiaoguang Zou +3 more
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On the Lie enveloping algebra of a pre-Lie algebra [PDF]
Journal of K-Theory, 2008 AbstractWe construct an associative product on the symmetric module S(L) of any pre-Lie algebra L. It turns S(L) into a Hopf algebra which is isomorphic to the enveloping algebra of LLie. Then we prove that in the case of rooted trees our construction gives the Grossman-Larson Hopf algebra, which is known to be the dual of the Connes-Kreimer Hopf ...
Oudom, J.-M., Guin, D.
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Some remarks on the Akivis algebras and the Pre-Lie algebras [PDF]
Czechoslovak Mathematical Journal, 2011 In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gröbner-Shirshov bases for free Pre-Lie algebras and the universal enveloping non-associative algebra of an Akivis algebra, respectively. As applications, we show I.P. Shestakov's result that any Akivis algebra is linear and D.
Chen, Yuqun, Li, Yu
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Families of Hopf algebra of trees and pre-lie algebras [PDF]
Homology, Homotopy and Applications, 2006 Using methods from math-ph/9907010, we study families of Hopf algebra structures on coloured trees.
Laan, Pepijn van der, Moerdijk, Ieke
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From Rota–Baxter algebras to pre-Lie algebras [PDF]
Journal of Physics A: Mathematical and Theoretical, 2007 23 pages, appear in Journal of Physics A; Mathematical and ...
An, Huihui, Bai, Chengming
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Embedding of Pre-Lie Algebras into Preassociative Algebras [PDF]
Algebra Colloquium, 2020 With the help of Rota–Baxter operators and Gröbner–Shirshov bases, we prove that every pre-Lie algebra can be injectively embedded into its universal enveloping preassociative algebra.
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The Universal Pre-Lie–Rinehart Algebras of Aromatic Trees [PDF]
, 2021 20 pages, improvements and clarifications added, 1 ...
Fløystad, Gunnar +2 more
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Degenerations of pre-Lie algebras [PDF]
Journal of Mathematical Physics, 2009 We consider the variety of pre-Lie algebra structures on a given n-dimensional vector space. The group GLn(K) acts on it, and we study the closure of the orbits with respect to the Zariski topology. This leads to the definition of pre-Lie algebra degenerations.
Burde, Dietrich, Benes, Thomas
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Twisted pre-Lie algebras of finite topological spaces [PDF]
Communications in Algebra, 2021 In this paper, we first study the species of finite topological spaces recently considered by F. Fauvet, L. Foissy, and D. Manchon. Then, we construct a twisted pre-Lie structure on the species of connected finite topological spaces. The underlying pre-Lie structure defines a coproduct on the species of finite topological spaces different from those ...
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