INDEX THEORY AND TOEPLITZ ALGEBRAS ON ONE-PARAMETER SUBGROUPS OF LIE-GROUPS

We form the Toeplitz C*-algebra T(G; X) associated to the one-parameter subgroup exp(tX) defined by a left-invariant vector field X on a compact Lie group G. We compute the K-theory of T(G, X) and its commutator ideal C(G; X). We also define an abstract analytical index for T(G; X) and show that this analytical index can be computed in terms of topological data.