Yetter-Drinfel'd categories associated to an arbitrary bialgebra

DOI10.1016/0022-4049(93)90114-9zbMath0796.16033OpenAlexW1972026565MaRDI QIDQ686109

Jacob Towber, David E. Radford

Publication date: 29 September 1994

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(93)90114-9

zbMATH Keywords

Hopf algebrabraided algebraleft \(A\)-comoduleprebraidingweakly braided algebraYetter-Drinfeld structure

Mathematics Subject Classification ID

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Cites Work

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• The Yang-Baxter equation and invariants of links
• Duality, crossing and MacLane's coherence
• Algebraic aspects of the quantum Yang-Baxter equation
• Solutions to the quantum Yang-Baxter equation and the Drinfel'd double
• Braided compact closed categories with applications to low dimensional topology
• Modular transformations for tensor categories
• Minimal quasitriangular Hopf algebras
• Free Hopf algebras generated by coalgebras
• QUASITRIANGULAR HOPF ALGEBRAS AND YANG-BAXTER EQUATIONS
• Quantum groups and representations of monoidal categories
• Two dual classes of bialgebras related to the concepts of “quantum group” and “quantum lie algebra”
• Doubles of quasitriangular hopf algebras

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