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2020•Quaestiones MathematicaeRequires access

The schur multiplier of a nilpotent Lie algebra with derived subalgebra of maximum dimension

Farangis Johari, Peyman Niroomand, Afsaneh Shamsaki

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Abstract

We give a new bound for the dimension of the Schur multiplier of an n-dimensional nilpotent Lie algebra of class c with the derived subalgebra of dimension n − 2. This new bound sharpens the earlier upper bounds on the dimension of Schur multiplier of such Lie algebras, especially for Lie algebras of maximal class.

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What this paper is about

We give a new bound for the dimension of the Schur multiplier of an n-dimensional nilpotent Lie algebra of class c with the derived subalgebra of dimension n − 2. This new bound sharpens the earlier upper bounds on the dimension of Schur multiplier of such Lie algebras, especially for Lie algebras of maximal class.

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Available abstract

We give a new bound for the dimension of the Schur multiplier of an n-dimensional nilpotent Lie algebra of class c with the derived subalgebra of dimension n − 2. This new bound sharpens the earlier upper bounds on the dimension of Schur multiplier of such Lie algebras, especially for Lie algebras of maximal class.

Key concepts: Mathematics, Schur multiplier, Subalgebra, Cartan subalgebra, Schur's lemma, Lie conformal algebra, Pure mathematics, Schur algebra

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