Lie bialgebra structures on the extended affine Lie algebra sl _2(C _q)? are investigated. In particular, all Lie bialgebra structures on sl _2(C _q)? are shown to be triangular coboundary. This result is obtained by employing some techniques, which may also work for more general extended affine Lie algebras, to prove the triviality of the first cohomology group of sl _2(C _q)? with coefficients in the tensor product of its adjoint module, namely, H1(sl _2(C _q)?,sl _2(C _q)??sl _2(C _q)?)=0.
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