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On dimension of the Schur multiplier of nilpotent Lie algebras

100%

Niroomand P.

Open Mathematics

2011

tom 9

nr 1

57-64

Let L be an n-dimensional non-abelian nilpotent Lie algebra and $$ s(L) = \frac{1} {2}(n - 1)(n - 2) + 1 - \dim M(L) $$ 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.

Commutator algebras arising from splicing operations

84%

Sverchkov S.

Open Mathematics

2014

tom 12

nr 11

1687-1699

We prove that the variety of Lie algebras arising from splicing operation coincides with the variety CM of centreby-metabelian Lie algebras. Using these Lie algebras we find the minimal dimension algebras generated the variety CM and the variety of its associative envelope algebras. We study the splicing n-ary operation. We show that all n-ary (n > 2) commutator algebras arising from this operation are nilpotent of index 3. We investigate the generalization of the splicing n-ary operation, and we formulate a series of open problems.

Ograniczanie wyników

2 Open Mathematics

1 Niroomand P.

1 Sverchkov S.

1 2014

1 2011

Wyniki wyszukiwania

On dimension of the Schur multiplier of nilpotent Lie algebras

Commutator algebras arising from splicing operations