Algebra Seminar

In this talk I will describe a recent result giving the decomposition of the tensor product of two irreducible representations of the quantum superalgebra osp(1|2) at roots of 1 and describe an application of this result to topological invariants of three-manifolds. The decomposition is the first for any quantum superalgebra at a root of unity and means that at roots of unity quantum osp(1|2) is an `almost modular Hopf superalgebra': a slightly weakened (and supersymmetric) version of Reshetikhin and Turaev's `modular Hopf algebras', used to create invariants of three-manifolds.