Schur indices in GAP: wedderga 4.6+

TL;DR

This paper introduces algorithms implemented in the GAP package wedderga 4.6+ for computing local and global Schur indices of characters and algebras, facilitating advanced algebraic computations.

Contribution

It presents new algorithms and their implementation for calculating Schur indices in GAP, enhancing computational tools for algebraic research.

Findings

Algorithms successfully compute Schur indices for various algebraic structures.

Implementation improves efficiency and accuracy of calculations in GAP.

Provides accessible tools for researchers in algebra and number theory.

Abstract

We describe a algorithms and their implementations that calculate local and global Schur indices of ordinary irreducible characters of finite groups, cyclotomic algebras over abelian number fields, and rational quaternion algebras. These functions are available with the latest release of the GAP package wedderga, versions 4.6 and higher.