Hi Nicolas,
Thanks for your comments!
I'm looking forward to your tutorial!
Best,
Jia
On Thu, Sep 1, 2011 at 11:15 AM, Nicolas M. Thiery
<nicolas.thi...@u-psud.fr> wrote:
> Hi Jia!
>
> On Wed, Aug 31, 2011 at 08:21:37PM -0500, Jia Huang wrote:
>> Thanks for your reply! I can get the 0-Hecke algebras from
>>
>> H = IwahoriHeckeAlgebraT("A2",0)
>>
>> But how to construct other similar algebras, such as the one
>> generated by T1, T2, satisfying the relations
>>
>> T1^3 = T1, T2^2 = T2, T1T2T1T2 = T2T1T2T1 ?
>
> So far, our algebras (and monoids) are all implemented "concretely",
> either by defining them by some generators in some ambient space, or
> by implementing explicitely the product rule. However, Simon King is
> implementing an interface with the letterplace library from Singular
> which should, among other things, allow for implementing in Sage an
> algebra by generators and relations:
>
> http://trac.sagemath.org/sage_trac/ticket/7797
>
> Anne has played with this patch, and may have more comments. I don't
> remember if she used it for finite or infinite dimensional algebras.
>
>
>> I looked at the files in
>> sage.categories.examples
>
> Good starting point :-)
>
>> But I didn't find any construction of an algebra there.
>
> You can, for example, look at:
>
> sage: HopfAlgebrasWithBasis(QQ).example()
> An example of Hopf algebra with basis: the group algebra of the Dihedral
> group of order 6 as a permutation group over Rational Field
>
> I'll try to write in the coming days a quick tutorial about what can
> currently be computed, representation theory wise, for finite
> dimensional algebras, and in particular algebras of finite monoids.
> It hasn't changed much since FPSAC ...
>
> Cheers,
> Nicolas
> --
> Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
> http://Nicolas.Thiery.name/
>
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