Multiply Fibred Manifolds

This paper aimed at investigating the product of longitudinal pseudo differential operators of C^*- algebras _ (=1) ^r_c^ (-) (F_) contained in C^*-closure (_c^ (-)) (F) by fibrations manifolds. Such that {F_} is a family of fibred manifolds. A locally homogenous condition of foliations is required to obtain us a generator of foliation F. this condition equivalent to requiring that Lie subalgebras generate Lie algebra. we also show a brief application of noncommutative harmonic analysis for compact Lie groups. This paper aimed at investigating the product of longitudinal pseudo differential operators of C^*- algebras _ (=1) ^r_c^ (-) (F_) contained in C^*-closure (_c^ (-)) (F) by fibrations manifolds. Such that {F_} is a family of fibred manifolds. A locally homogenous condition of foliations is required to obtain us a generator of foliation F. this condition equivalent to requiring that Lie subalgebras generate Lie algebra. we also show a brief application of noncommutative harmonic analysis for compact Lie groups.