TL;DR
This paper introduces Lie group-rack triples as a group-level generalization of Lie-Leibniz triples, extending the integration process from Leibniz algebras to Lie groups.
Contribution
It defines Lie group-rack triples and demonstrates their integration from finite-dimensional Lie-Leibniz triples, generalizing existing algebraic structures.
Findings
Defined Lie group-rack triples as tangent structures of Lie-Leibniz triples.
Established a method to integrate finite-dimensional Lie-Leibniz triples into local Lie group-rack triples.
Abstract
In this paper, we introduce the group version of a Lie-Leibniz triple, which we call a Lie group-rack triple. We define a Lie group-rack triple whose tangent structure is a Lie-Leibniz triple, which is a generalization of an augmented Lie rack whose tangent structure is an augmented Leibniz algebra. We show that any finite-dimensional Lie-Leibniz triple can be integrated to a local Lie group-rack triple by generalizing the integration procedure of an augmented Leibniz algebra into an augmented Lie rack.
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