TY - JOUR

T1 - Hopf algebras constructed by the FRT-construction

AU - Towber, Jacob

AU - Westreich, Sara

PY - 2009/5

Y1 - 2009/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=58849146080&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2008.09.012

DO - 10.1016/j.jpaa.2008.09.012

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:58849146080

SN - 0022-4049

VL - 213

SP - 772

EP - 782

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 5

ER -