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2011•arXiv (Cornell University)Open access

Schur Multipliers of Nilpotent Lie Algebras

Lindsey Bosko, Stitzinger, Ernie L.

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Abstract

We consider the Schur multipliers of finite dimensional nilpotent Lie algebras. If the algebra has dimension greater than one, then the Schur multiplier is non-zero. We give a direct proof of an upper bound for the dimension of the Schur multiplier as a function of class and the minimum number of generators of the algebra. We then compare this bound with another known bound.

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We consider the Schur multipliers of finite dimensional nilpotent Lie algebras. If the algebra has dimension greater than one, then the Schur multiplier is non-zero. We give a direct proof of an upper bound for the dimension of the Schur multiplier as a function of class and the minimum number of generators of the algebra. We then compare this bound with another known bound.

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Available abstract

We consider the Schur multipliers of finite dimensional nilpotent Lie algebras. If the algebra has dimension greater than one, then the Schur multiplier is non-zero. We give a direct proof of an upper bound for the dimension of the Schur multiplier as a function of class and the minimum number of generators of the algebra. We then compare this bound with another known bound.

Key concepts: Schur multiplier, Mathematics, Schur algebra, Schur's lemma, Schur's theorem, Lie conformal algebra, Pure mathematics, Nilpotent group

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