Crossed Modules and Quantum Groups in Braided Categories |
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Authors: | Yu. N. Bespalov |
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Affiliation: | (1) Institute for Theoretical Physics, Metrologichna str., 14-b, Kiev 143, 252143, Ukraine. e-mail |
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Abstract: | Let A be a Hopf algebra in a braided category . Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group the corresponding braided category of modules is identified with a full subcategory in . The connection with cross products is discussed and a suitable cross product in the class of quantum braided groups is built. Majid–Radford theorem, which gives equivalent conditions for an ordinary Hopf algebra to be such a cross product, is generalized to the braided category. Majid's bosonization theorem is also generalized. |
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Keywords: | braided category braided Hopf algebra crossed module quantum braided group |
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