Abstract
In this paper, we give a sufficient condition for double crossproductX ⋈A to beX ⋈ τ A for some skew pairingτ ifX ⋈A is a 2-cocycle deformation ofX ⊗A. Then we give a sufficient and necessary condition forX ⋈A to beX ⋈ τ A by using natural isomorphism terminology.
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References
C Kassel. Quantum groups. New York: Springer-Verlag, 1995
S Majid. Quasitriangular Hopf algebras and Yang-Baxter equations. Internat J Modern Physics, 1990, A5(1): 1–91
Y Doi. Braided bialgebras and quadratic bialgebras. Comm in Algebra, 1993, 21(5): 1731–1749
Y Doi, M Takeuchi. Multiplication alteration by two-cocycles-the quantum version. Comm in Algebra, 1994, 22(14): 5715–5732
M E Sweedler. Hopf Algebras. New York: Benjamin, 1969
S Montgomery. Hopf algebras and their actions on rings. CBMS, Series in Math 82, AMS, 1993
R Larson, J Towber. Two dual classes of bialgebras related to the concepts of “quantum groups” and “quantum Lie algebras”. Comm in Algebra, 1991, 19(12): 3295–3345
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Chen, H. Skew pairing, Cocycle deformations and double crossproducts. Acta Mathematica Sinica 15, 225–234 (1999). https://doi.org/10.1007/BF02650666
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DOI: https://doi.org/10.1007/BF02650666