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We study the Yangians Y(a) associated with the simple Lie algebras a of type B, C or D. The algebra Y(a) can be regarded as a quotient of the extended Yangian X(a) whose defining relations are written in an R-matrix form. In this paper we are concerned with the algebraic structure and representations of the algebra X(a). We prove an analog of the Poincaré-Birkhoff-Witt theorem for X(a) and show that the Yangian Y(a) can be realized as a subalgebra of X(a). Furthermore, we give an independent proof of the classification theorem for the finite-dimensional irreducible representations of X(a) which implies the corresponding theorem of Drinfeld for the Yangians Y(a). We also give explicit constructions for all fundamental representation of the Yangians.

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We introduce two subalgebras in the type A quantum affine algebra which are coideals with respect to the Hopf algebra structure. In the classical limit q → 1 each subalgebra specializes to the enveloping algebra U(k), where k is a fixed point subalgebra of the loop algebra gl N [λ, λ −1 ] with respect to a natural involution corresponding to the embedding of the orthogonal or symplectic Lie algebra into gl N . We also give an equivalent presentation of these coideal subalgebras in terms of generators and defining relations which have the form of reflection-type equations. We provide evaluation homomorphisms from these algebras to the twisted quantized enveloping algebras introduced earlier by Gavrilik and Klimyk and by Noumi. We also construct an analog of the quantum determinant for each of the algebras and show that its coefficients belong to the center of the algebra. Their images under the evaluation homomorphism provide a family of central elements of the corresponding twisted quantized enveloping algebra.