Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cyclic cohomology of certain nuclear Fr\'echet and DF algebras   We give explicit formulae for the continuous Hochschild and cyclic homology
and cohomology of certain topological algebras. To this end we show that, for a
continuous morphism $\phi: \X\to \Y$ of complexes of complete nuclear
$DF$-spaces, the isomorphism of cohomology groups $H^n(\phi): H^n(\X) \to
H^n(\Y)$ is automatically topological. The continuous cyclic-type homology and
cohomology are described up to topological isomorphism for the following
classes of biprojective $\hat{\otimes}$-algebras: the tensor algebra $E
\hat{\otimes} F$ generated by the duality $(E, F, < \cdot, \cdot >)$ for
nuclear Fr\'echet spaces $E$ and $F$ or for nuclear $DF$-spaces $E$ and $F$;
nuclear biprojective K\"{o}the algebras $\lambda(P)$ which are Fr\'echet spaces
or $DF$-spaces; the algebra of distributions $\mathcal{E}^*(G)$ on a compact
Lie group $G$.

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The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
16
The categories of this paper are: stat
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom