Operator Algebras, Tensor Categories and Tensor Networks in Topological Order

Explore the intersection of operator algebras, tensor categories, and tensor networks in this lecture on quantum symmetries and two-dimensional topological order in condensed matter physics. Delve into the application of operator algebra techniques, particularly the Jones theory of subfactors, to study tensor category structures. Discover how bi-unitary connections, a form of generalized quantum 6j-symbols, serve as powerful finite-dimensional tools for analyzing these structures. Examine various applications in the theory of two-dimensional topological order and their relevance to mathematical theories of topological quantum computations. Gain insights into how these advanced mathematical concepts contribute to our understanding of new symmetries in physics.

Yasuyuki Kawahigashi: Operator algebras, tensor categories and tensor networks #ICBS2024