Hi Jia,
Yes, I played with Simon King's patch and it worked well for what I needed.
I will be in Minnesota September 18-21, so we can talk more then (it might be
easier than by e-mail) in case the other implementations do not work for you.
Best,
Anne
On 9/1/11 9:15 AM, Nicolas M. Thiery 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
--
You received this message because you are subscribed to the Google Groups
"sage-combinat-devel" group.
To post to this group, send email to sage-combinat-devel@googlegroups.com.
To unsubscribe from this group, send email to
sage-combinat-devel+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/sage-combinat-devel?hl=en.
