Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Courant algebroids and Poisson Geometry   Given a manifold M with an action of a quadratic Lie algebra d, such that all
stabilizer algebras are co-isotropic in d, we show that the product M\times d
becomes a Courant algebroid over M. If the bilinear form on d is split, the
choice of transverse Lagrangian subspaces g_1, g_2 of d defines a bivector
field on M, which is Poisson if (d,g_1,g_2) is a Manin triple. In this way, we
recover the Poisson structures of Lu-Yakimov, and in particular the Evens-Lu
Poisson structures on the variety of Lagrangian Grassmannians and on the de
Concini-Procesi compactifications. Various Poisson maps between such examples
are interpreted in terms of the behaviour of Lagrangian splittings under
Courant morphisms.

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The categories of this paper are: hep-lat
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The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin