Displaying similar documents to “On the cohomology of nilpotent Lie algebras”

On a nilpotent Lie superalgebra which generalizes Q.

José María Ancochea Bermúdez, Otto Rutwig Campoamor (2002)

Revista Matemática Complutense

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In Gilg (2000, 2001) the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra L are studied and classified in low dimensions. Here we consider a class of superalgebras whose even part is the filiform, naturally graded Lie algebra Q, which only exists in even dimension as a consequence of the centralizer property....

On dimension of the Schur multiplier of nilpotent Lie algebras

Peyman Niroomand (2011)

Open Mathematics

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Let L be an n-dimensional non-abelian nilpotent Lie algebra and s ( L ) = 1 2 ( n - 1 ) ( n - 2 ) + 1 - dim M ( L ) where M(L) is the Schur multiplier of L. In [Niroomand P., Russo F., A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra (in press)] it has been shown that s(L) ≥ 0 and the structure of all nilpotent Lie algebras has been determined when s(L) = 0. In the present paper, we will characterize all finite dimensional nilpotent Lie algebras with s(L) = 1; 2.

Some properties of complex filiform Lie algebras.

F. J. Echarte Reula, J. R. Gómez Martín, J. Núñez Valdés (1992)

Extracta Mathematicae

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The purpose of this paper is to study some properties of Filiform Lie Algebras (FLA) and to prove the following theorem: a FLA, of dimension n, is either derived from a Solvable Lie Algebra (SLA) of dimension n+1 or not derived from any LA.

Invariants of Lie color algebras acting on graded algebras

Jeffrey Bergen, Piotr Grzeszczuk (2000)

Colloquium Mathematicae

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We prove a series of "going-up" theorems contrasting the structure of semiprime algebras and their subalgebras of invariants under the actions of Lie color algebras.

An overview of free nilpotent Lie algebras

Pilar Benito, Daniel de-la-Concepción (2014)

Commentationes Mathematicae Universitatis Carolinae

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Any nilpotent Lie algebra is a quotient of a free nilpotent Lie algebra of the same nilindex and type. In this paper we review some nice features of the class of free nilpotent Lie algebras. We will focus on the survey of Lie algebras of derivations and groups of automorphisms of this class of algebras. Three research projects on nilpotent Lie algebras will be mentioned.

Cohomology ring of n-Lie algebras.

Mikolaj Rotkiewicz (2005)

Extracta Mathematicae

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Natural graded Lie brackets on the space of cochains of n-Leibniz and n-Lie algebras are introduced. It turns out that these brackets agree under the natural embedding introduced by Gautheron. Moreover, n-Leibniz and n-Lie algebras turn to be canonical structures for these brackets in a similar way in which associative algebras (respectively, Lie algebras) are canonical structures for the Gerstenhaber bracket (respectively, Nijenhuis-Richardson bracket).