On distributive laws in derived bracket construction and homotopy theory of derived bracket Leibniz algebras
K. Uchino
TL;DR
This paper introduces Lie-Leibniz algebras as a new algebraic structure derived from the derived bracket construction, proves their operad is Koszul, and explores their homotopy versions with new results on sh Lie and sh Leibniz algebras.
Contribution
It defines Lie-Leibniz algebras, proves their operad is Koszul, and discusses their strong homotopy versions, advancing the understanding of derived brackets in homotopy theory.
Findings
Lie-Leibniz operad is Koszul
Development of strong homotopy derived bracket Leibniz algebras
New results on sh Lie and sh Leibniz algebras
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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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models