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

Allen Herman; Gabriela Olteanu; Angel del Rio

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

Representation Theory 2007-10-05 v1 Rings and Algebras

Authors: Allen Herman , Gabriela Olteanu , Angel del Rio

Abstract

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.

Keywords

Schur group cyclic cyclotomic algebras abelian extension cyclotomic extensions finite index

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@article{arxiv.0710.1027,
  title  = {The gap between the Schur group and the subgroup generated by cyclic cyclotomic algebras},
  author = {Allen Herman and Gabriela Olteanu and Angel del Rio},
  journal= {arXiv preprint arXiv:0710.1027},
  year   = {2007}
}

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12 pages

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

Abstract

Keywords

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