Operator Algebras, Topology and Subgroups of Quantum Symmetry – Construction of Subgroups of Quantum Groups –

Abstract

In this article, we will discuss several interactions between the non commutative Galois problems, i.e., inclusions of operator algebras and topological quantum field theory in three dimensions. Those interactions are shown to be concretely solved and are related to both the quantum subgroups of the quantum group $SU(2)_N$ at the deformation parameter $q = \exp (2\pi i/N)$.