Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representations and cohomologies of Hom-pre-Lie algebras   In this paper, first we study dual representations and tensor representations
of Hom-pre-Lie algebras. Then we develop the cohomology theory of Hom-pre-Lie
algebras in term of the cohomology theory of Hom-Lie algebras. As applications,
we study linear deformations of Hom-pre-Lie algebras, which are characterized
by the second cohomology groups of Hom-pre-Lie algebras with the coefficients
in the regular representation. The notion of a Nijenhuis operator on a
Hom-pre-Lie algebra is introduced which can generate trivial linear
deformations of a Hom-pre-Lie algebra. Finally, we introduce the notion of a
Hessian structure on a Hom-pre- Lie algebra, which is a symmetric nondegenerate
2-cocycle with the coefficient in the trivial representation. We also introduce
the notion of an $\huaO$-operator on a Hom-pre-Lie algebra, by which we give an
equivalent characterization of a Hessian structure.

4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th