Higher Indicators for the Doubles of some Totally Orthogonal Groups

Abstract

We investigate the indicators for certain groups of the form $\BZ_k\rtimes D_l$ and their doubles, where $D_l$ is the dihedral group of order $2l$. We subsequently obtain an infinite family of totally orthogonal, completely real groups which are generated by involutions, and whose doubles admit modules with second indicator of -1. This provides us with answers to several questions concerning the doubles of totally orthogonal finite groups.

28 pages

References in corpus (2)

• Central Invariants and Frobenius-Schur Indicators for Semisimple Quasi-Hopf Algebras
• Computing Higher Indicators for the Double of a Symmetric Group