Reference: Derivations on the $(2n+1)$-dimensional Heisenberg algebra

Question

I am looking for a reference (either a book or a paper) which treats the $(2n+1)$-dimensional Heisenberg Lie algebra $\mathfrak h_n$ (see Wikipedia: Heisenberg group for the definition). More particularly, I am looking for a reference in which the space $\mathrm{Der}(\mathfrak h_n)$ is determined.

This is of course not difficult to do by hand, but I would guess that this is fairly well-known, so I would rather just refer to some previous work than include the details of it in my own work.

@DietrichBurde Wonderful, thanks! (It's no rush, so you can look it up whenever you find the time) — MSDG, Nov 12 '19 at 12:24

score 1 · Accepted Answer · answered Nov 12 '19 at 14:29

1

The derivations of the $(2n+1)$-dimensional Heisenberg Lie Algebra have been determined, for example, here in Proposition $9$. The case $n=1$ has been computed at this site here:

Examples of derivation of Lie algebras

answered Nov 12 '19 at 14:29

Dietrich Burde

130,978

Excellent! Exactly what I was looking for. Many thanks – MSDG Nov 12 '19 at 14:33

Reference: Derivations on the $(2n+1)$-dimensional Heisenberg algebra

1 Answers1