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- W3145536161 abstract "Let $A$ be a Hopf algebra in a braided category $cal C$. Crossed modules over $A$ are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category $DY{cal C}^A_A$ 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 $(A,overline A,{cal R})$ the corresponding braided category of modules ${cal C}_{cO{A,overline A}}$ is identified with a full subcategory in $DY{cal C}_A^A$. 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." @default.
- W3145536161 created "2021-04-13" @default.
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- W3145536161 date "1995-10-12" @default.
- W3145536161 modified "2023-09-27" @default.
- W3145536161 title "Crossed modules and quantum groups in braided categories" @default.
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