Derived bracket construction and Manin products

Details Derived bracket construction and Manin products Derived bracket construction and Manin products

2009-04-13

arxiv.org/abs/0904.1961v7

Mathematics

Quantum Algebra

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Scientific paper

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.

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