Sebastian Halbig
Título: A non-semisimple Kitaev lattice model
Resumen: The Kitaev lattice model is a proposed model for quantum computation with error-correction implemented on a physical level. Classically, this is achieved as follows. One fixes a closed surface S and a semisimple complex Hopf algebra H. Given a CW-decomposition of S, one defines a representation of the Drinfeld double of H. Using integrals and cointegrals one shows that its invariant subspace is a topological invariant: its dimension does not depend on the chosen decomposition but only on the genus of S and the Hopf algebra H. In this talk, based on joint work with A. Hirmer, U.Krähmer, C. Meusburger, and T. Voss, we provide a pedagogical introduction to the model and explain how to extend it to the non-semisimple setting. We present a new approach to proving topological invariance based on bitensor products and centred around a variant of excision.