第二讲： 2026年1月9日（周五）下午14:00

摘要: I will give a series of two introductory lectures on the use of Hopf algebra methods in quantum many body physics, with an emphasis on applications in topological order and (non-invertible) matrix product operator (MPO) symmetries.

In the first lecture, I begin by showing that the axioms of Hopf algebra naturally emerge in the study of MPO symmetries in 1D quantum spin chains (subject to a mild tractability condition). I will then cover the basics of Hopf algebra theory, including its representation theory and the relation to fusion categories. I will also briefly mention the application in 1D exactly solvable models.

In the second lecture I will talk about quasitriangular Hopf algebras and the application in 2D topological order. The key viewpoint here is that quasitriangular Hopf algebras naturally lead to a second quantized theory of (non-Abelian) anyons, where the fusion and braiding of anyons are encoded in the algebra of their creation and annihilation operators. Kitaev's quantum double models will be explained as primary examples.