Eric Nordberg asked the following questions.
HI, I am trying to do computations in group algrabras. Mostly, using
groups such as s3 (permuations in three places.) Is there any decent
way to define an algebra of this sort, seeing as how the permuations do not
form a ring. If not, is there any way to define addition for
permuations, so that I can psuedo form my own algebra? If neither of
these work, are there any other suggestions with gap?
The proper way to define group algebras in GAP is to put the group
elements into records, and to define addition, subtraction, multiplication,
powering and so on for these records.
It depends on the sort of computations one has in mind how many facilities
one really needs to provide for group algebra elements and group algebras.
About two years ago Philip Osterlund wrote some nice GAP code for computing
in group algebras.
If he does not object then I will put this as a package into the 'incoming'
directory on our server, and then inform you about this.