Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Serre-Swan theorem for non-commutative C$^{*}$-algebras   We generalize the Serre-Swan theorem to non-commutative C$^{*}$-algebras. For
a Hilbert C$^{*}$-module $X$ over a C$^{*}$-algebra ${\cal A}$, we introduce a
hermitian vector bundle $\exx$ associated to $X$. We show that there is a
linear subspace $\Gamma_{X}$ of the space of all holomorphic sections of ${\cal
E}_{X}$ and a flat connection $D$ on ${\cal E}_{X}$ with the following
properties: (i) $\Gamma_{X}$ is a Hilbert ${\cal A}$-module with the action of
${\cal A}$ defined by $D$, (ii) the C$^{*}$-inner product of $\Gamma_{X}$ is
induced by the hermitian metric of ${\cal E}_{X}$, (iii) ${\cal E}_{X}$ is
isomorphic to an associated bundle of an infinite dimensional Hopf bundle, (iv)
$\Gamma_{X}$ is isomorphic to $X$.

35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas