Crossed modules and quantum groups in braided categories I

Details Crossed modules and quantum groups in braided categories I Crossed modules and quantum groups in braided categories I

1994-08-18

arxiv.org/abs/hep-th/9408102v1

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, 20 figures

Scientific paper

Let $H$ be a Hopf algebra in braided category $\cal C$. Crossed modules over $H$ are objects with both module and comodule structures satisfying some comatibility condition. Category ${\cal C}^H_H$ of crossed modules is braided and is concrete realization of general categorical construction. For quantum braided group $(H,{\cal R})$ corresponding braided category ${\cal C}^{\cal R}_H$ of modules is identifyed with full subcategory in ${\cal C}_H^H$. Connection with crossproducts is discussed. Correct cross product in the class of quantum braided groups is built. Radford's--Majid's theorem gives equivalent condition for usual Hopf algebra to be crossproduct. Braided variant and analog of this theorem for quantum braided qroups are obtained.

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