
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 -racks and generalize several results known on racks. In particular, we show that the tangent space of a Lie -Rack at the neutral element has a Leibniz -algebra structure. We also define a cohomology theory of -racks..
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Taxonomy
TopicsConstraint Satisfaction and Optimization
