On dimension of the Schur multiplier of nilpotent Lie algebras

Peyman Niroomand

Open Mathematics (2011)

  • Volume: 9, Issue: 1, page 57-64
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Peyman Niroomand. "On dimension of the Schur multiplier of nilpotent Lie algebras." Open Mathematics 9.1 (2011): 57-64. <http://eudml.org/doc/269221>.

@article{PeymanNiroomand2011,
abstract = {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.},
author = {Peyman Niroomand},
journal = {Open Mathematics},
keywords = {Schur multiplier; Nilpotent Lie algebras; nilpotent Lie algebra},
language = {eng},
number = {1},
pages = {57-64},
title = {On dimension of the Schur multiplier of nilpotent Lie algebras},
url = {http://eudml.org/doc/269221},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Peyman Niroomand
TI - On dimension of the Schur multiplier of nilpotent Lie algebras
JO - Open Mathematics
PY - 2011
VL - 9
IS - 1
SP - 57
EP - 64
AB - 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.
LA - eng
KW - Schur multiplier; Nilpotent Lie algebras; nilpotent Lie algebra
UR - http://eudml.org/doc/269221
ER -

References

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