# On distributive laws in derived bracket construction and homotopy theory of derived bracket Leibniz algebras

Source: [On distributive laws in derived bracket construction and homotopy theory of derived bracket Leibniz algebras](<https://www.sota2.com/research/paper/68fa50321e209131ce9694d9>)

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

Data updated: 2025-10-25T10:42:40.616Z

Authors: K. Uchino

Published: 2011-10-19T05:38:37.000Z

## Abstract

We introduce a new type of algebra, which is called a Lie-Leibniz algebra. This concept is an abstraction of derived bracket construction. It will be proved that the operad of Lie-Leibniz algebras is Koszul. The strong homotopy version of derived bracket Leibniz algebras will be discussed. We will get some new results with respect to sh Lie and sh Leibniz algebras.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1110.4188>)

[PDF](<https://arxiv.org/pdf/1110.4188.pdf>)