Higher Indicators for the Doubles of Some Totally Orthogonal Groups

Abstract

We investigate the indicators for certain groups of the form ℤ _k  ⋊ 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.

Key Words:

• Drinfeld double
• Groups
• Hopf algebras
• Indicators
• Quantum algebra

2010 Mathematics Subject Classification:

• Primary 16T05
• Secondary 16D99, 20C99

Notes

The exact isomorphism type of this subgroup depends on the group G, but will not be needed here.

Communicated by M. Cohen.