On the cyclic homology of commutative algebras over arbitrary ground rings |
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Authors: | Guillermo Cortiñas |
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Institution: | Dep. De Matemática , Fac.Cs.Exactas , Calle 50 Y115, La Plata, 1900, Argentina |
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Abstract: | Abstract Let D(H) be the quantum double associated to a finite dimensional quasi-Hopf algebra H, as in Hausser and Nill ((Hausser, F., Nill, F. (1999a). Diagonal crossed products by duals of quasi-quantum groups. Rev. Math. Phys. 11:553–629) and (Hausser, F., Nill, F. (1999b). Doubles of quasi-quantum groups. Comm. Math. Phys. 199:547–589)). In this note, we first generalize a result of Majid (Majid, S. (1991). Doubles of quasitriangular Hopf algebras. Comm. Algebra 19:3061–3073) for Hopf algebras, and then prove that the quantum double of a finite dimensional quasitriangular quasi-Hopf algebra is a biproduct in the sense of Bulacu and Nauwelaerts (Bulacu, D., Nauwelaerts, E. (2002). Radford's biproduct for quasi-Hopf algebras and bosonization. J. Pure Appl. Algebra 179:1–42.). |
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Keywords: | Quasitriangular quasi-Hopf algebras Quantum double Braided Hopf algebras Biproduct |
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