Bouarroudj, Sofiane, Grozman, Pavel, Leites, Dimitry (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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María Ronco (2011)
Annales de l’institut Fourier
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The goal of our work is to study the spaces of primitive elements of some combinatorial Hopf algebras, whose underlying vector spaces admit linear basis labelled by subsets of the set of maps between finite sets. In order to deal with these objects we introduce the notion of shuffle algebras, which are coloured algebras where composition is not always defined. We define bialgebras in this framework and compute the subpaces of primitive elements associated to them. These spaces of primitive...
L. M. Camacho, J. R. Gómez, A. J. González (2005)
Extracta Mathematicae
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The knowledge of the natural graded algebras of a given class of Lie algebras offers essential information about the structure of the class. So far, the classification of naturally graded Lie algebras is only known for some families of p-filiform Lie algebras. In certain sense, if g is a naturally graded Lie algebra of dimension n, the first case of no p-filiform Lie algebras it happens when the characteristic sequence is (n-3,2,1). We present the classification of a particular family...
Campoamor-Stursberg, Rutwig (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Grozman, P., Leites, D., Poletaeva, E. (2002)
Homology, Homotopy and Applications
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Skrypnyk, Taras V. (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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McRae, Alan S. (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Fialowski, Alice, de Montigny, Marc (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Klaus Bering, Tom Lada (2009)
Archivum Mathematicum
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We look at two examples of homotopy Lie algebras (also known as algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators to verify the homotopy Lie data is shown to produce the same results.