LIE n-RACKS

TL;DR

This paper introduces Lie n-racks, a new algebraic structure generalizing racks, and explores their properties, including tangent space structures and cohomology theories, expanding the mathematical framework of racks.

Contribution

It defines Lie n-racks, establishes their tangent space as Leibniz n-algebras, and develops a cohomology theory for n-racks, extending existing rack theory.

Findings

Tangent space of Lie n-racks forms Leibniz n-algebras

Defined a cohomology theory for n-racks

Generalized results known for racks to Lie n-racks

Abstract

In this paper, we introduce the category of Lie $n$-racks and generalize several results known on racks. In particular, we show that the tangent space of a Lie $n$-Rack at the neutral element has a Leibniz $n$-algebra structure. We also define a cohomology theory of $n$-racks..