C-cross products and a generalized mechanical N-body problem

Abstract

For each finite dimensional real vector space X we construct a C*-algebra A graded by the lattice of all subspaces of X and we compute its quotient with respect to the algebra of compact operators. This allows one to describe the essential spectrum and to prove the Mourre estimate for the self-adjoint operators affiliated to A.

Keywords

• C*-cross product
• N-body problem
• Mourre estimate.