Racks, Leibniz algebras and Yetter-Drinfel'd modules

Abstract

A Hopf algebra object in Loday and Pirashvili's category of linear maps entails an ordinary Hopf algebra and a Yetter-Drinfel'd module. We equip the latter with a structure of a braided Leibniz algebra. This provides a unified framework for examples of racks in the category of coalgebras discussed recently by Carter, Crans, Elhamdadi and Saito.

arXiv comment20 pages, no figures

References in corpus (2)

• Leibniz algebras, Lie racks, and digroups
• Deformation quantization of Leibniz algebras

Cited by in corpus (1)

• Lie Algebroids in the Loday-Pirashvili Category