# Derived bracket construction and Manin products

Source: [Derived bracket construction and Manin products](<https://www.sota2.com/research/paper/68fa51d21e209131ce976710>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:55:35.471Z

Authors: K. Uchino

Published: 2009-04-13T19:28:58.000Z

## Abstract

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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0904.1961>)

[PDF](<https://arxiv.org/pdf/0904.1961.pdf>)