Semisimple Hopf algebras and fusion categories


Galindo, C. (2017). Semisimple Hopf algebras and fusion categories. Perimeter Institute. https://pirsa.org/17070062


Galindo, Cesar. Semisimple Hopf algebras and fusion categories. Perimeter Institute, Jul. 31, 2017, https://pirsa.org/17070062


          @misc{ pirsa_17070062,
            doi = {},
            url = {https://pirsa.org/17070062},
            author = {Galindo, Cesar},
            keywords = {Quantum Foundations, Quantum Information},
            language = {en},
            title = {Semisimple Hopf algebras and fusion categories},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {jul},
            note = {PIRSA:17070062 see, \url{https://pirsa.org}}


This talk will be a short introduction to the semisimple Hopf algebras over an algebraically closed field of characteristic 0 and their representation theories. It is intended to outline the main basic results about structure and known methods for the construction of semisimple Hopf algebras: extensions, twisting, Tannakian reconstruction. Basic notions concerning tensor categories will be introduced: braided structures, center construction, fiber functors. Special emphasis is given to the notion of fusion category. At the same time, the relations between these notions and those of the Hopf algebras are studied.