Algorithms to construct minimal left group codes are provided. These are based on results describing a complete set of orthogonal primitive idempotents in each Wedderburn component of a semisimple… (More)

We present an alternative constructive proof of the Brauer–Witt theorem using the so-called strongly monomial characters that gives rise to an algorithm for computing the Wedderburn decomposition of… (More)

We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each… (More)

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… (More)

We give an explicit and character-free construction of a complete set of orthogonal primitive idempotents of a rational group algebra of a finite nilpotent group and a full description of the… (More)

We present an algorithm to compute the Wedderburn decomposition of semisimple group algebras based on a computational approach of the Brauer-Witt theorem. The algorithm was implemented in the GAP… (More)

We characterize the maximum r-local index of a Schur algebra over an abelian number field K in terms of global information determined by the field K, for r an arbitrary rational prime. This completes… (More)

The algebras of Kleinian type are finite dimensional semisimple rational algebras A such that the group of units of an order in A is commensurable with a direct product of Kleinian groups. We… (More)