Search results for "Homology of Lie algebra"

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Some criteria for detecting capable Lie algebras

2013

Abstract In virtue of a recent bound obtained in [P. Niroomand, F.G. Russo, A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra 39 (2011) 1293–1297], we classify all capable nilpotent Lie algebras of finite dimension possessing a derived subalgebra of dimension one. Indirectly, we find also a criterion for detecting noncapable Lie algebras. The final part contains a construction, which shows that there exist capable Lie algebras of arbitrary big corank (in the sense of Berkovich–Zhou).

Discrete mathematicsPure mathematicsAlgebra and Number TheoryHeisenberg algebraNon-associative algebranilpotent Lie algebrasKilling formAffine Lie algebraGraded Lie algebraLie conformal algebraNilpotent Lie algebraSettore MAT/02 - AlgebraAdjoint representation of a Lie algebraRepresentation of a Lie groupcorankHomology of Lie algebraMathematicsJournal of Algebra
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A restriction on the schur multiplier of nilpotent lie algebras

2011

An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier M(L) of a finite dimensional nilpotent Lie algebra L. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maximal dimension. This allows precision on the size of M(L). Among other results, applications to the non-abelian tensor square L ⊗ L are illustrated.

Discrete mathematicsPure mathematicsAlgebra and Number TheorySchur multiplierSchur's lemmanilpotent Lie algebrasSchur algebrahomology of Lie algebraSchur's theoremLie conformal algebraNilpotent Lie algebraSettore MAT/02 - AlgebraAdjoint representation of a Lie algebraRepresentation of a Lie groupNilpotent groupMathematics::Representation TheoryMathematics
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