Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Star products on graded manifolds and $\alpha'$-corrections to double
  field theory   Originally proposed as an $O(d,d)$-invariant formulation of classical closed
string theory, double field theory (DFT) offers a rich source of mathematical
structures. Most prominently, its gauge algebra is determined by the so-called
C-bracket, a generalization of the Courant bracket of generalized geometry, in
the sense that it reduces to the latter by restricting the theory to solutions
of a "strong constraint". Recently, infinitesimal deformations of these
structures in the string sigma model coupling $\alpha'$ were found. In this
short contribution, we review constructing the Drinfel'd double of a Lie
bialgebroid and offer how this can be applied to reproduce the C-bracket of DFT
in terms of Poisson brackets. As a consequence, we are able to explain the
$\alpha'$-deformations via a graded version of the Moyal-Weyl product in a
class of examples. We conclude with comments on the relation between $B$- and
$\beta$-transformations in generalized geometry and the Atiyah algebra on the
Drinfel'd double.

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The categories of this paper are: hep-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc