Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On para-K\"ahler Lie algebroids and generalized pseudo-Hessian
  structures   In this paper, we generalize all the results obtained on para-K\"ahler Lie
algebras in Journal of Algebra {\bf 436} (2015) 61-101 to para-K\"ahler Lie
algebroids. In particular, we study exact para-K\"ahler Lie algebroids as a
generalization of exact para-K\"ahler Lie algebras. This study leads to a
natural generalization of pseudo-Hessian manifolds. Generalized pseudo-Hessian
manifolds have many similarities with Poisson manifolds. We explore these
similarities which, among others, leads to a powerful machinery to build
examples of non trivial pseudo-Hessian structures. Namely, we will show that
given a finite dimensional commutative and associative algebra
$(\mathcal{A},.)$, the orbits of the action $\Phi$ of $(\mathcal{A},+)$ on
$\mathcal{A}^*$ given by $\Phi(a,\mu)=\exp(L_a^*)(\mu)$ are pseudo-Hessian
manifolds, where $L_a(b)=a.b$. We illustrate this result by considering many
examples of associative commutative algebras an show that the pseudo-Hessian
manifolds obtained are very interesting.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc