2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230680We develop the theory of semisimple weak Hopf algebras and obtain analogues of a number of classical results for ordinary semisimple Hopf algebras. We prove a criterion for semisimplicity and analyze the square of the antipode S^2 of a semisimple weak Hopf algebra A. We explain how the Frobenius-Perron dimensions of irreducible A-modules and eigenvalues of S^2 can be computed using the inclusion matrix associated to A. A trace formula of Larson and Radford is extended to a relation between the global and Frobenius-Perron dimensions of A. Finally, an analogue of the Class Equation of Kac and Zhu is established and properties of $A$-module algebras and their dimensions are studied.Ams-latex, 24 pages, an error in Proposition 3.4.2 is correctedQuantum AlgebraRings and Algebrastext