Results 41 to 50 of about 2,546 (128)
A rigidity theorem for pre-Lie algebras
Journal of Pure and Applied Algebra, 2006 The starting point of the paper under review is the classical Leray theorem that any graded connected commutative and cocommutative Hopf algebra is a free commutative algebra and a free cocommutative coalgebra and its analogues for unital infinitesimal bialgebras [\textit{J.-L. Loday} and \textit{M. Ronco}, J. Reine Angew. Math.
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On crossed modules of pre-Lie algebras
Journal of Algebra and Its ApplicationsGiven a Lie algebra [Formula: see text] and a [Formula: see text]-module [Formula: see text], it is due to Gerstenhaber that there is an isomorphism between [Formula: see text] and the group of equivalence classes of crossed modules with kernel [Formula: see text] and cokernel [Formula: see text].
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Pre-Lie algebras and the rooted trees operad
, 2000 A Pre-Lie algebra is a vector space L endowed with a bilinear product * : L \times L to L satisfying the relation (x*y)*z-x*(y*z)= (x*z)*y-x*(z*y), for all x,y,z in L. We give an explicit combinatorial description in terms of rooted trees of the operad associated to this type of algebras and prove that it is a Koszul operad.
Chapoton, Frédéric, Livernet, Muriel
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Compatible anti-pre-Lie algebras
Journal of Algebra and Its ApplicationsIn this paper, we introduce the notion of compatible anti-pre-Lie algebras and study relationship between them and the related structures such as anti-[Formula: see text]-operators, commutative [Formula: see text]-cocycles on compatible Lie algebras.
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Pre-Lie Algebras, Their Multiplicative Lattice, and Idempotent Endomorphisms
We introduce the notions of pre-morphism and pre-derivation for arbitrary non-associative algebras over a commutative ring $k$ with identity. These notions are applied to the study of pre-Lie $k$-algebras and, more generally, Lie-admissible $k$-algebras.
Cerqua, Michela, Facchini, Alberto
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Lie and pre-Lie theory of Novikov algebras
Novikov algebras provide a simple but powerful algebraic axiomatization of important features of classical diferential calculus. We study their structure properties, modeling their relationships with commutative algebras with a derivation, featuring the role of their Lie and pre-Lie structures and analyzing the structure of their enveloping algebras ...
Bandiera, Ruggero, Patras, Frédéric
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Hopf algebras of trees and pre-Lie structures
, 2011 We investigate in this thesis the Hopf algebra structure on the vector space H spanned by the rooted forests, associated with the pre-Lie operad. The space of primitive elements of the graded dual of this Hopf algebra is endowed with a left pre-Lie product denoted by ⊲, defined in terms of insertion of a tree inside another.
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Fast gradient algorithm for complex ICA and its application to the MIMO systems. [PDF]
Sci Rep, 2023 Mika D.
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Infinitesimal bialgebras, pre-Lie and dendriform algebras
, 2002 We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal bialgebra. We show that they correspond to modules and bimodules over the infinitesimal version of the double. We show that there is a natural, but non-obvious way to construct a pre-Lie algebra from an arbitrary infinitesimal bialgebra and a dendriform ...
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