Lie-admissible algebras and operads

By Michel Goze, Elisabeth Remm. 2002

87 citations recorded by the source corpus.

Abstract A Lie-admissible algebra gives a Lie algebra by anticommutativity. In this work we describe remarkable types of Lie-admissible algebras such as Vinberg algebras, pre-Lie algebras or Lie algebras. We compute the corresponding binary quadratic operads and study their duality. Considering Lie algebras as Lie-admissible algebras, we can define for each Lie algebra a cohomology with values in an Lie-admissible module. This leads to the study some deformations of Lie algebras in the classes of Lie-admissible algebras.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/03a7d4f7cac1a4c7f03977445561bf8f58666c2e

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On Hom-algebra structures (2006, background): “The G-associative algebra in classical case was studied in [3].”
Algebras with one operation including Poisson and other Lie-admissible algebras (2004, methodology): “Above we saw an algebra admitting a one-parametric family of non-equivalent monoidal structures.”
Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras (2009, methodology): “In Section 2, we introduce Hom-associative superalgebras and Hom-Lie superalgebras.”
Rota–Baxter Hom-Lie–Admissible Algebras (2011, background): “The latter are twisted generalizations of the G-associative algebras introduced in [39].”
Poisson algebras in terms of non-associative algebras (2008, background): “Poisson algebras are Lie-admissible power-associative algebras.”
Paradigm of Nonassociative Hom-algebras and Hom-superalgebras (2010, methodology): “This study borders also an extension to graded case of the Lieadmissible algebras discussed in [21].”