Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lie algebras and Lie groups over noncommutative rings   The aim of this paper is to introduce and study Lie algebras and Lie groups
over noncommutative rings. For any Lie algebra $\gg$ sitting inside an
associative algebra $A$ and any associative algebra $\FF$ we introduce and
study the algebra $(\gg,A)(\FF)$, which is the Lie subalgebra of $\FF \otimes
A$ generated by $\FF \otimes \gg$. In many examples $A$ is the universal
enveloping algebra of $\gg$. Our description of the algebra $(\gg,A)(\FF)$ has
a striking resemblance to the commutator expansions of $\FF$ used by M.
Kapranov in his approach to noncommutative geometry. To each algebra $(\gg,
A)(\FF)$ we associate a ``noncommutative algebraic'' group which naturally acts
on $(\gg,A)(\FF)$ by conjugations and conclude the paper with some examples of
such groups.

31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc