A Hopf algebra with four generators among which an involution (reflection) operator, is introduced. The defining relations involve commutators and anticommutators. The discrete series representations are developed. Designated by sl_-1(2), this algebra encompasses the Lie superalgebra osp(1|2). It is obtained as a q=-1 limit of the sl_q(2) algebra and seen to be equivalent to the parabosonic oscillator algebra in irreducible representations. It possesses a noncocommutative coproduct. The

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... Gordan coefficients (CGC) of sl_-1(2) are obtained and expressed in terms of the dual -1 Hahn polynomials. A generating function for the CGC is derived using a Bargmann realization.