A K-theoretic approach to the classification of symmetric spaces

We show that the classification of the symmetric spaces can be achieved by K-theoretical methods. We focus on Hermitian symmetric spaces of non-compact type, and define K-theory for JB*-triples along the lines of C*-theory. K-groups have to be provided with further invariants in order to classify. Among these are the cycles obtained from so called grids, intimately connected to the root systems of an underlying Lie-algebra and thus reminiscent of the classical classification scheme.