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...g algebra • U q(sl2), as defined in [14, §23.1.1] and we are not aware of any relationship between these bases. It would also be interesting to compare our bases with the ones announced by Fan Qin in =-=[16, 17]-=-. Finally, it should be noted that John Foster constructed in [8] a basis of Uq(sl2) which differs from (1.1) in that Chebyshev polynomials C(m) are replaced by Cm. We establish properties of Bsl2 in ...