Pre-Lie algebras, also called Vinberg algebras, have become an important tool in combinatorics, differential geometry, the theory of operads and in various application domains such as perturbative quantum field theory or numerical analysis, to quote only a few. They generate a special class of Lie...
In this paper, we introduce the notion of a pre-Lie 2-algebra, which is acategorification of a pre-Lie algebra. 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 ...
The notion of non-abelian phase space of a Lie algebra was first formulated and then discussed by Kuperschmidt. In this paper, we further study the non-abe... BAI,CHENGMING - 《Reviews in Mathematical Physics》 被引量: 38发表: 2006年 A FURTHER STUDY ON NON-ABELIAN PHASE SPACES:: LEFT-...
We give a simple characterization of Lie elements in free pre-Lie algebras as elements of the kernel of a map between spaces of trees. 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 Lo...
of weight zero on the infinite dimensional 3-Lie algebra Aω=⟨Lm|m∈Z⟩ to construct 3-Pre-Lie algebras Bk, 0⩽k⩽4, and we subsequently discuss the structure. It is shown that B2 and B4 are non-isomorphic simple 3-Pre-L...
We also show that symmetric brace algebras and pre-Lie algebras are the same. Finally, we give a similar interpretation of the Hopf algebra of planar rooted trees.关键词: <span class="Ttl">Key Words</span>brace algebra Hopf algebra pre-Lie algebra rooted tree ...
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...
(2.2) For a pre-Lie algebra A, the commutator [38] [x, y] = xy − yx, (2.3) defines a Lie algebra G = G(A), which is called the sub-adjacent Lie algebra of A. For any x, y ∈ A, let Lx and Rx denote the left and right multiplication operator respectively, that is, ...
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 ...
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