# [sage-combinat-devel] Re: End(CombinatorialFreeModule)?


On Thursday, December 6, 2012 at 12:47:53 PM UTC, Dima Pasechnik wrote:
>
> On 2012-12-06, Nicolas M. Thiery <nicolas.thi...@u-psud.fr> wrote:
> > On Thu, Dec 06, 2012 at 07:29:57AM +0000, Dima Pasechnik wrote:
> >> I wonder if one can actually work in the endomorphism ring/algebra of a
> >> CombinatorialFreeModule, and if yes, how.
> >
> > Not yet. I guess the closest approximation would be to take V \otimes V.
> > But of course it is not endowed with composition, and it should really
> > be V^* \otimes V (which makes a difference in non finite dimension).
> >
> >> Examples most appreciated. (Ideally, I would like to know how to
> >> work with algebras specified by multiplication coefficients in this
> >> framework)
> >
> > I am not sure what you mean. Can you be a bit more specific?
> say, I have a permutation group acting on the basis elements of a
> CombinatorialFreeModule, and I want to get hold of the endomorphisms
> commuting with this action. Then it would be natural to represent
> the ring of such endomorphisms by the multiplication coefficients.
> (i.e. construct a regular representation of this ring).
>
>
Another canonical example of "natural" regular representations is the
quotient of a polynomial ring over a 0-dimensional ideal.
Frankly, it is astonishing that given all the amount of stuff one can do
with "combinatorial algebras", this is overlooked; this is perhaps the most
basic example of use of linear algebra in computational algebraic geometry,
after all.


> Best,
> Dima
>
>
> >
> > Cheers,
> >                                 Nicolas
> > --
> > Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
> > http://Nicolas.Thiery.name/
> >
>
>

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