Hopf algebras constructed by the FRT-construction |
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| Authors: | Jacob Towber |
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| Affiliation: | a Department of Mathematics, De Paul University, Chicago, IL, United States
b Interdisciplinary Department of the Social Sciences, Bar-Ilan University, Ramat-Gan, Israel |
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| Abstract: | Given any bialgebra A and a braiding product 〈|〉 on A, a bialgebra U〈|〉 was constructed in [R. Larson, J. Towber, Two dual classes of bialgebras related to the concepts of “quantum group” and “quantum Lie algebra”, Comm. Algebra 19 (1991) 3295-3345], contained in the finite dual of A. This construction generalizes a (not very well known) construction of Fadeev, Reshetikhin and Takhtajan [L.D. Faddeev, N.Yu. Reshetikhin, L.A. Takhtajan, Quantum Groups. Braid Group, Knot Theory and Statistical Mechanics, in: Adv. Ser. Math. Phys., vol. 9, World Sci. Publishing, Teaneck, NJ, 1989, pp. 97-110]. In the present paper it is proved that when U〈|〉 is finite-dimensional (even if A is not), then it is a quasitriangular Hopf algebra. |
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| Keywords: | Primary 16W30 17B37 |
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