Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A universal formula for representing Lie algebra generators as formal
  power series with coefficients in the Weyl algebra   Given a $n$-dimensional Lie algebra $g$ over a field $k \supset \mathbb Q$,
together with its vector space basis $X^0_1,..., X^0_n$, we give a formula,
depending only on the structure constants, representing the infinitesimal
generators, $X_i = X^0_i t$ in $g\otimes_k k [[t]]$, where $t$ is a formal
variable, as a formal power series in $t$ with coefficients in the Weyl algebra
$A_n$. Actually, the theorem is proved for Lie algebras over arbitrary rings
$k\supset Q$.
  We provide three different proofs, each of which is expected to be useful for
generalizations. The first proof is obtained by direct calculations with
tensors. This involves a number of interesting combinatorial formulas in
structure constants. The final step in calculation is a new formula involving
Bernoulli numbers and arbitrary derivatives of coth(x/2). The dimensions of
certain spaces of tensors are also calculated. The second method of proof is
geometric and reduces to a calculation of formal right-invariant vector fields
in specific coordinates, in a (new) variant of formal group scheme theory. The
third proof uses coderivations and Hopf algebras.

5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int