Minimal Faithful Representation of the Heisenberg Lie Algebra with Abelian Factor

Abstract

For a finite dimensional Lie algebra $\g$ over a field $\k$ of characteristic zero, the $\mu$-function (respectively ${\mu }_{nil}$-function) is defined to be the minimal dimension of $V$ such that $\g$ admits a faithful representation (respectively a faithful nilrepresentation) on $V$. Let $\h_m$ be the Heisenberg Lie algebra of dimension $2m+1$ and let ${\mathfrak{a}}_n$ be the abelian Lie algebra of dimension $n$. The aim of this paper is to compute $μ(\h_m \oplus \mathfrak{a}_n)$ and $μ_{nil}(\h_m \oplus \mathfrak{a}_n)$ for all $m,n\in \mathbb{N}$.

8 pages

References in corpus (1)

• Faithful Representations of Minimal Dimension of 6-dimensional nilpotent Lie algebras

Cited by in corpus (2)

• Faithful Representations of Minimal Dimension of 6-dimensional nilpotent Lie algebras
• A lower bound for faithful representations of nilpotent Lie algebras