A Note on the Schur Multiplier of a Nilpotent Lie Algebra

By Peyman Niroomand, Francesco Russo. 2010

71 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c661461ed35f6f046866363c09a79db4eb14fce3

Citations in the corpus

• Some criteria for detecting capable Lie algebras (2013, unknown): “Moreover, we combine the results which we obtain with some other results in [20] and are able to prove a necessary and sufficient condition of capability for nilpotent finite dimensional Lie algebras with small derived subalgebra L2, namely dim L2 = 1.”