Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derived bracket construction and Manin products   We will extend the classical derived bracket construction to any algebra over
a binary quadratic operad. We will show that the derived product construction
is a functor given by the Manin white product with the operad of permutation
algebras. As an application, we will show that the operad of prePoisson
algebras is isomorphic to Manin black product of the Poisson operad with the
preLie operad. We will show that differential operators and Rota-Baxter
operators are, in a sense, Koszul dual to each other.

6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph