Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantized symplectic actions and W-algebras   With a nilpotent element in a semisimple Lie algebra g one associates a
finitely generated associative algebra W called a W-algebra of finite type.
This algebra is obtained from the universal enveloping algebra U(g) by a
certain Hamiltonian reduction. We observe that W is the invariant algebra for
an action of a reductive group G with Lie algebra g on a quantized symplectic
affine variety and use this observation to study W. Our results include an
alternative definition of W, a relation between the sets of prime ideals of W
and of the corresponding universal enveloping algebra, the existence of a
one-dimensional representation of W in the case of classical g and the
separation of elements of W by finite dimensional representations.

14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol