[GAP Forum] How to construct a group algebra by generators using function Algebra(Field, generators) ?

[Alexander Konovalov]

Dear Dong,

you can construct the desired group algebra as follows:

gap> GroupRing( GF(2), SymmetricGroup(3) );
<algebra-with-one over GF(2), with 2 generators>

See the description of the 'GroupRing' function at
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP063.htm#SSEC001.2

In your attempt to construct it using Algebra, first, z is a field
element and not a field, as required. Moreover, as it is written on
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP060.htm#SSEC001.1,
the second argument must be a list of vectors. This is in brief why
you can not construct the group algebra with "Algebra".

Note that there are several GAP packages extending the system's
functionality for group rings: Wedderga, LAGUNA and Unitlib, see
http://www.gap-system.org/Packages/packages.html

Hope this helps, and please do not hesitate to ask further questions.

Best wishes,
Alexander



On 09 Apr 2007, at 12:17, Dong Jingcheng wrote:

> Dear forum:
> I want to construct  a group algebra kS3 by generators using   
> function Algebra(Field,generators),but it cannot work.My program is  
> listed below:
> z:=Z(2);
> A:=Algebra(z,[(1,2),(1,2,3)]);
>
> Where (1,2) and (1,2,3) generate the group S3.What  shall I do?
>
> Thank you!
> Dong