Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pre-symplectic algebroids and their applications   In this paper, we introduce the notion of a pre-symplectic algebroid, and
show that there is a one-to-one correspondence between pre-symplectic
algebroids and symplectic Lie algebroids. This result is the geometric
generalization of the relation between left-symmetric algebras and symplectic
(Frobenius) Lie algebras. Although pre-symplectic algebroids are not
left-symmetric algebroids, they still can be viewed as the underlying
structures of symplectic Lie algebroids. %We study three classes of
pre-symplectic algebroids in detail. Then we study exact pre-symplectic
algebroids and show that they are classified by the third cohomology group of a
left-symmetric algebroid. Finally, we study para-complex pre-symplectic
algebroids. Associated to a para-complex pre-symplectic algebroid, there is a
pseudo-Riemannian Lie algebroid. The multiplication in a para-complex
pre-symplectic algebroid characterizes the restriction to the Lagrangian
subalgebroids of the Levi-Civita connection in the corresponding
pseudo-Riemannian Lie algebroid.

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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol