A Note on the Schur Multiplier of a Nilpotent Lie Algebra

Abstract

For a nilpotent Lie algebra L of dimension n and dim (L ²) = m ≥ 1, we find the upper bound , where M(L) denotes the Schur multiplier of L. In case m = 1, the equality holds if and only if L ≅ H(1) ⊕ A, where A is an abelian Lie algebra of dimension n − 3 and H(1) is the Heisenberg algebra of dimension 3.

Key Words:

• Nilpotent Lie algebras
• Schur Multiplier

2000 Mathematics Subject Classification:

• Primary 17B30
• Secondary 17B60, 17B99

ACKNOWLEDGMENT

The authors are grateful to the referee, who noted the importance of [4] and [10] in the context of the present article.

Notes

Communicated by P. Tiep.