A comment on the integration of Leibniz algebras

TL;DR

This paper clarifies that the universal enveloping dialgebra for Leibniz algebras aligns with their interpretation as generalizations of the adjoint representation of Lie algebras, simplifying their integration.

Contribution

It demonstrates that the formal integration of Leibniz algebras is straightforward when viewed as generalizations of Lie algebra adjoint representations.

Findings

Universal enveloping dialgebra definition is consistent with Leibniz as a generalization of Lie adjoint.

Integration problem of Leibniz algebras is essentially trivial.

Provides a new perspective on Leibniz algebra integration.

Abstract

In this note we point out that the definition of the universal enveloping dialgebra for a Leibniz algebra is consistent with the interpretation of a Leibniz algebra as a generalization not of a Lie algebra, but of the adjoint representation of a Lie algebra. From this point of view, the formal integration problem of Leibniz algebras is, essentially, trivial.