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# GAP package Wedderga
The title
"Wedderga" stands
for "Wedderburn decomposition of group algebras".
This
is a GAP package
to compute the simple components
of the Wedderburn
decomposition
of semisimple group algebras. So the main functions
of the
package returns a list
of simple algebras whose direct sum
is isomorphic
to
the group algebra given
as input.
The methods implemented by the package produces the Wedderburn decomposition
of a group algebra FG provided G
is a finite group
and F
is either a finite
field
of characteristic coprime
with the order
of G,
or an abelian number
field (i.e. a subfield
of a finite cyclotomic extension
of the rationals).
Other functions
of Wedderga compute the primitive central idempotents
of
semisimple group algebras
and a complete
set of orthogonal primitive
idempotents,
and calculate Schur indices
of simple algebras.
The package also provides functions
to construct crossed products over a
group
with coefficients
in an associative ring
with identity
and the
multiplication determined by a given action
and twisting.
Furthermore, the package provides functions
to create code words from a group
ring element.
Wedderga does
not use external binaries
and, therefore, works without
restrictions on the
type of the operating system. It
is redistributed
with
GAP, but
is not loaded by default. Therefore,
to use Wedderga, first you need
to load it using the following command:
gap> LoadPackage(
"wedderga");
Gurmeet Kaur Bakshi, Osnel Broche Cristo, Allen Herman, Olexandr Konovalov,
Sugandha Maheshwary, Aurora Olivieri, Gabriela Olteanu, Ángel del Río
and
Inneke Van Gelder.
