Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some semi-direct products with free algebras of symmetric invariants   Let $\mathfrak g$ be a complex reductive Lie algebra and $V$ the underling
vector space of a finite-dimensional representation of $\mathfrak g$. Then one
can consider a new Lie algebra $\mathfrak q=\mathfrak g{\ltimes} V$, which is a
semi-direct product of $\mathfrak g$ and an Abelian ideal $V$. We outline
several results on the algebra $\mathbb C[\mathfrak q^*]^{\mathfrak q}$ of
symmetries invariants of $\mathfrak q$ and describe all semi-direct products
related to the defining representation of $\mathfrak{sl}_n$ with $\mathbb
C[\mathfrak q^*]^{\mathfrak q}$ being a free algebra.

20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol