Notes on Leibniz $n$-algebras

TL;DR

This paper investigates the properties of certain functors on Leibniz n-algebras and explores their implications for homology and universal central extensions, advancing the theoretical understanding of these algebraic structures.

Contribution

It provides new insights into the behavior of forgetful and Daletskii-Takhtajan functors on Leibniz n-algebras and applies these to homology and central extensions.

Findings

Analysis of functor behaviors on perfect objects and crossed modules

Applications to homology of Leibniz n-algebras

Results on universal central extensions

Abstract

We analyze behaviors of generalized forgetful and Daletskii-Takhtajan's functors on perfect objects and crossed modules of Leibniz $n$-algebras. Then we give applications to homology and universal central extensions of Leibniz $n$-algebras.