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. ThiƩry "Isil" <nthi...@users.sf.net> 
> > http://Nicolas.Thiery.name/ 
> > 

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