Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simplicial homology of strong semilattices of Banach algebras   Certain semigroups are known to admit a `strong semilattice decomposition'
into simpler pieces. We introduce a class of Banach algebras that generalise
the $\ell^1$-convolution algebras of such semigroups, and obtain a
disintegration theorem for their simplicial homology. Using this we show that
for any Clifford semigroup $S$ of amenable groups, $\lp{1}(S)$ is simplicially
trivial: this generalises results in \cite{YC_GMJ}. Some other applications are
presented.

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The categories of this paper are: stat
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th