Discrete $C^*$-Frobenius Algebras and Infinite-Index Extensions in Algebraic Quantum Field Theories
We introduce discrete $C^*$-Frobenius algebras as categorical data for constructing infinite-index extensions of M\"{o}bius covariant nets. The underlying representation is a countable direct sum of simple dualized modules, while the direct sum itself is not necessarily dualizable. Accordingly, rather than requiring a...