On Hopf 2-algebras

Details On Hopf 2-algebras On Hopf 2-algebras

2009-08-17

arxiv.org/abs/0908.2353v2

Mathematics

Group Theory

26 pages, clarification of several statements

Scientific paper

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.

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