Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebras of symbols associated with the Weyl calculus for Lie group
  representations   We develop our earlier approach to the Weyl calculus for representations of
infinite-dimensional Lie groups by establishing continuity properties of the
Moyal product for symbols belonging to various modulation spaces. For instance,
we prove that the modulation space of symbols $M^{\infty,1}$ is an associative
Banach algebra and the corrresponding operators are bounded. We then apply the
abstract results to two classes of representations, namely the unitary
irreducible representations of nilpotent Lie groups, and the natural
representations of the semidirect product groups that govern the magnetic Weyl
calculus. The classical Weyl-H\"ormander calculus is obtained for the
Schr\"odinger representations of the finite-dimensional Heisenberg groups, and
in this case we recover the results obtained by J.~Sj\"ostrand in 1994.

30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn