Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Hopf algebras and their Hopf-cyclic cohomology   A natural extension of the Hopf-cyclic cohomology, with coefficients, is
introduced to encompass topological Hopf algebras. The topological theory
allows to work with infinite dimensional Lie algebras. Furthermore, the
category of coefficients (AYD modules) over a topological Lie algebra and those
over its universal enveloping (Hopf) algebra are isomorphic. For topological
Hopf algebras, the category of coefficients is identified with the
representation category of a topological algebra called the anti-Drinfeld
double. Finally, a topological van Est type isomorphism is detailed, connecting
the Hopf-cyclic cohomology to the relative Lie algebra cohomology with respect
to a maximal compact subalgebra.

29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph