They generate a special class of Lie algebras and have enveloping algebras enjoying more properties than usual enveloping algebras of Lie algebras.doi:10.1007/978-3-030-77845-3_6Cartier, PierreInstitut des Hautes Études ScientifiquesPatras, FrédéricUniversité Côte d’AzurAlgebra and Applications...
We recover some recent results by Dotsenko, Shadrin and Vallette on theDeligne groupoid of a pre-Lie algebra, showing that they follow naturally by apre-Li... B Ruggero - 《International Mathematics Research Notices》 被引量: 17发表: 2013年 加载更多来源...
We prove that the category of pre-Lie2-algebras and the category of 2-term pre-Lie$_\\infty$-algebras are equivalent.We classify skeletal pre-Lie 2-algebras by the third cohomology of a pre-Liealgebra. We prove that crossed modules of pre-Lie algebras are in one-to-onecorrespondence ...
We explain how this result is related to natural operations on the Chevalley-Eilenberg complex of a Lie algebra. We also indicate a possible relation to Loday's theory of triplettes. 关键词: Mathematics - Algebraic Topology Mathematics - K-Theory and Homology DOI: doi:10.1142/S0218216507005208...
We construct an associative product on the symmetric moduleS(L) of any pre-Lie algebraL. It turnsS(L) into a Hopf algebra which is isomorphic to the enveloping algebra ofLLie. Then we prove that in the case of rooted trees our construction gives the Grossman-Larson Hopf algebra, which is...
We show that the quantisation of a connected simply-connected Poisson-Lie group admits a left-covariant noncommutative differential structure at lowest deformation order if and only if the dual of its Lie algebra admits a pre-Lie algebra structure. As an example, we find a pre-Lie algebra struc...
hopfalgebrastreesliefamiliesalgebra a r X i v : m a t h / 0 4 0 2 0 2 2 v 1 [ m a t h . Q A ] 2 F e b 2 0 0 4FamiliesofHopfalgebrasoftrees andpre-Liealgebras PepijnvanderLaanandIekeMoerdijk 1stFebruary2008 Abstract Usingmethodsfrom[10],westudyfamiliesofHopfalgebrastructures ...
Some subclasses of pre-Lie algebras are very important: Definition 2.2 Let A be a pre-Lie algebra. (1) If A has no ideals except itself and zero, then A is called simple. A is called semisimple if A is the direct sum of simple pre-Lie algebras [15, 16]. (2) If for every x ...
We construct an associative product on the symmetric module S(L) of any pre-Lie algebra L. Then we proove that in the case of rooted trees our construction is dual to that of Connes and Kreimer. We also show that symmetric brace algebras and pre-Lie alge
The concept of weighted infinitesimal unitary bialgebra is an algebraic meaning of the nonhomogenous associative Yang–Baxter equation. In this paper, we equip the space of decorated planar rooted forests with a coproduct which makes it a weighted infinitesimal unitary bialgebra. Further, we construct...