On Hopf 2-algebras
Group Theory
2010-04-12 v2 Category Theory
Quantum Algebra
Abstract
Our main goal in this paper is to translate the diagram relating groups, Lie algebras and Hopf algebras to the corresponding 2-objects, i.e. to categorify it. This is done interpreting 2-objects as crossed modules and showing the compatibility of the standard functors linking groups, Lie algebras and Hopf algebras with the concept of a crossed module. One outcome is the construction of an enveloping algebra of the string Lie algebra of Baez-Crans, another is the clarification of the passage from crossed modules of Hopf algebras to Hopf 2-algebras.
Cite
@article{arxiv.0908.2353,
title = {On Hopf 2-algebras},
author = {Yael Fregier and Friedrich Wagemann},
journal= {arXiv preprint arXiv:0908.2353},
year = {2010}
}
Comments
26 pages, clarification of several statements