ON THE CLASSIFYING SPACE OF A COMPACT CONNECTED LIE GROUP

We show that a compact connected Lie group G is determined, up to isomorphism, by the homotopy type of its classifying space BG. This gives an affirmative answer to a question of G. Mislin [12]. Our proof depends on a purely algebraic result. This result is stated in section 2 and says that the Weyl group of G and its action on a maximal torus can be recovered from the lambda-structure of the complex K-theory of BG.