On distributive laws in derived bracket construction

Details On distributive laws in derived bracket construction On distributive laws in derived bracket construction

2011-10-19

arxiv.org/abs/1110.4188v3

Mathematics

Quantum Algebra

12 pages

Scientific paper

We will introduce new relations which naturally arises between Lie-operad and Leibniz-operad. We prove that the relations are "distributive laws" of the Lie operad over the Leibniz operad in the sense of M. Markl (1996). By using the distributive law, we define a new operad, which is called a Lie-Leibniz operad. The Lie-Leibniz operad is Koszul, because the Lie operad and the Leibniz operad are both Koszul. The Koszul dual operad of Lie-Leibniz operad is also studied. In addition, we will prove that the Lie-Leibniz operad naturally becomes a resolution over the Lie operad.

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