Abstract
We 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 categorical 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
