[GAP Forum] Cohomology of nontrivial G-modules?

[Benoit Jacob]

On Wed, Nov 11, 2015 at 4:30 PM, Dima Pasechnik <
dmitrii.pasechnik at cs.ox.ac.uk> wrote:

> On Wed, Nov 11, 2015 at 11:37:39AM -0500, Benoit Jacob wrote:
> > On Wed, Nov 11, 2015 at 11:34 AM, Dima Pasechnik <
> > dmitrii.pasechnik at cs.ox.ac.uk> wrote:
> >
> > > On Wed, Nov 11, 2015 at 10:52:29AM -0500, Benoit Jacob wrote:
> > > > I need to compute cohomology groups of the form
> > > >
> > > >     H^n(G, A)
> > > >
> > > > where G is a finite group and A is a nontrivial G-module. More
> > > > specifically, A is a finite-dimensional vector space over Z/2Z on
> which G
> > > > acts non-trivially.
> > > >
> > > > Any example code would be greatly appreciated; I searched for
> existing
> > > help
> > > > and documentation but only found examples dealing with trivial
> G-modules.
> > >
> > > did you look at GAP's packages? E.g.
> > > http://gap-system.org/Packages/hap.html
> > > seems to be just what you need.
> > >
> >
> > Thanks for the answer. HAP does seem like just what I need, but, being a
> > GAP beginner, I need something more pedestrian than the functions
> reference
> > documentation I see there. Is there any self-contained example code going
> > through the steps of defining a G-module, then computing its cohomology?
>
> did you look at http://hamilton.nuigalway.ie/Hap/www/ ?
> (it's more or less the 1st link on http://gap-system.org/Packages/hap.html
> )
> It has a section called Tutorial.
>

I did, buton first reading I missed where it showed how to define arbitrary
G-modules.
Now I see that GModuleByMats function in
http://hamilton.nuigalway.ie/Hap/www/SideLinks/About/aboutIntro.html

Thanks!
Benoit


> HTH,
> Dima
>