The gap between the Schur group and the subgroup generated by cyclic cyclotomic algebras

Herman, Allen; Olteanu, Gabriela; del Rio, Angel

The gap between the Schur group and the subgroup generated by cyclic cyclotomic algebras

Authors

Herman, Allen

Olteanu, Gabriela

del Rio, Angel

Description

Let $K$ be an abelian extension of the rationals. Let $S(K)$ be the Schur group of $K$ and let $CC(K)$ be the subgroup of $S(K)$ generated by classes containing cyclic cyclotomic algebras. We characterize when $CC(K)$ has finite index in $S(K)$ in terms of the relative position of $K$ in the lattice of cyclotomic extensions of the rationals.
12 pages