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Two groups G, H are said to be a matched pair if they act on each other and these actions, (a, /?), obey a certain compatibility condition. In such a situation one may form a bicrossproduct group, denoted Gβ cχiQ H. Also in this situation one may form a bicrossproduct Hopf, Hopf-von Neumann or Kac algebra obtained by simultaneous cross product and cross coproduct. We show that every compact semi-simple simply-connected Lie group G is a member of a matched pair, denoted (G, G*)9 in a natural way. As an example we construct the matched pair in detail in the case (SU(2), SU(2)*) where

Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations