چکیده (انگلیسی):

We use integrals of left coideal sub algebras to develop Harmonic analysis for semisimple Hopf algebras. We show how N∗, the space of functional on N, is embedded in H∗. We define a bilinear form on N∗ and show that irreducible N-characters are orthogonal with respect to that form. We then give an explicit formula for induced characters of N and show how the induced characters are embedded in R(H). In the second part we give an intrinsic definition for solvable semisimple Hopf algebras via left coideal sub algebras and their integrals. We show how this definition generalizes solvability for finite groups. In particular, commutative and nilpotent Hopf algebras are solvable. We finally prove an analogue of Burnside theorem: A semisimple quasitriangular Hopf alge-bras of dimension pa qb is solvable.