5
votes
1answer
279 views

History of Jordan Canonical Form?

Can anyone suggest a reference that discusses the history of the Jordan canonical form? In particular, I am interested in: When and how was it first stated? (I understand it was independently stated ...
6
votes
2answers
400 views

When did the meaning of the term “metabelian” change?

I just realised that the meaning of the term "metabelian", when applied to groups, or Lie algebras, seems to have changed over years. (These days, it means that $[[G,G],[G,G]]$ is trivial, while in ...
6
votes
1answer
207 views

Does the vanishing of the Poisson bracket on $S(\mathfrak{g})^{\mathfrak{g}}$ inspire the disover of Duflo's isomorphism theorem?

For any finite dimensional Lie algebra $\mathfrak{g}$, we know that the universal enveloping algebra $U(\mathfrak{g})$ is a deformation of the symmetric algebra $S(\mathfrak{g})$. In fact let's define ...
10
votes
1answer
455 views

Smallest dimension of nontrivial representation of a simple Lie algebra over `$\mathbb{C}$`

The question involved here is natural and very classical, but I'm unsure what has been formally stated and proved in the literature. The only approach I know involves assembling facts that apparently ...
4
votes
1answer
184 views

About the term “tangential derivation” on a free Lie algebra.

Let $\mathcal{lie}_n$ be the free Lie algebra generated by $n$ elements $x_1,\ldots, x_n$. A derivation $u\in \text{Der}(\mathcal{lie}_n)$ is called tangential if there exist $a_i\in \mathcal{lie}_n, ...
11
votes
1answer
709 views

So, did Poincaré prove PBW or not?

This seems to be a question whose answer depends on whom you ask. Maybe we can come up with a final answer? It is known that Poincaré, at least, invented something that can be called ...
20
votes
3answers
971 views

What was Casimir's precise role in describing the center of the universal enveloping algebra of a semisimple Lie algebra?

This question is prompted by a recent MO question on explicit computations of Weyl group invariants for certain exceptional simple Lie algebras: 37602. Like some others who started graduate study in ...