-
-
Notifications
You must be signed in to change notification settings - Fork 439
New issue
Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.
By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.
Already on GitHub? Sign in to your account
q-commuting polynomials #34412
Comments
Commit: |
comment:1
Here is a very simple implementation for them that feeds off as much as possible. Likely could be improved (e.g., not relying on New commits:
|
Branch pushed to git repo; I updated commit sha1. New commits:
|
This comment has been minimized.
This comment has been minimized.
comment:4
Bot is green. |
comment:5
ok, ok. I was just wondering for myself whether this fits into the setting of Ore algebras, and hence could be done using the "ore_algebra" package. |
comment:6
Thanks for looking at this. I didn't mean to pressure you into it. I thought about that too. However, that viewpoint makes one of the variables more special than the others, which is not desirable to me. For example, if we take two variables |
comment:7
is there any other structure on that algebra ? a coproduct or co-module structure ? With just x and y, this is sometimes called the quantum plane, right ? minor remark:
could create directly the tuple |
comment:8
Replying to @fchapoton:
I am not sure. I will do some searching.
Yes, it does. Should I add this as a comment to the doc? (Hopefully you can respond quickly as I will be leaving for home soon.)
It is actually (slightly) faster for whatever reason to do
Still remains completely counterintuitive to me. |
comment:9
So it doesn't seem like they are not known to carry any further natural structure since I can't find anything about that in this survey: https://link.springer.com/article/10.1007/BF02355445 Although we can build a comodule structure on them using the quantum coordinate ring of SLn as a generalization of exercise (3) in Section 3.4 of http://www.mate.unlp.edu.ar/~ggarcia/encuentros/notas-curso-qg-ha.pdf Maybe in Sage we should call them There is a slightly more general construction that could be done with |
comment:10
ok, let's not bother more. I am setting to positive. |
Reviewer: Frédéric Chapoton |
comment:12
Thank you. It’s definitely an interesting question as the classical case, and maybe even the related geometry, suggests that there should be additional structure (maybe also from the iterated Ore extensions). What do you think about the name though? Would you say A more trivial point but do you think I should add a quantum plane note to the doc before we merge this initial version? |
comment:13
oh, well, you can add a comment and set back to positive if you like. for the name, I am ok with "qCommutingPolynomials". As far as I know, neither of your proposed name is very standard |
comment:14
I feel lazy Thank you again. |
comment:15
yes, ok. In the same vein, an idea is that the Laurent version (quantum torus algebras) could be of interest to people doing cluster algebras. |
comment:16
That’s a good idea of something to implement. It is just a relatively small tweak of my code to use the |
comment:17
Follow is #34472. |
Changed branch from public/algebras/q_commute_polys-34412 to |
These show up in quantum mechanics computations and are a variation of skew commuting polynomials (cf. the exterior algebra) satisfying
yx = q^{B_xy} xy
for all variables that index fixed a skew symmetric bilinear matrixB
.We provide a simple initial implementation.
CC: @fchapoton
Component: algebra
Keywords: q-commuting polynomials
Author: Travis Scrimshaw
Branch/Commit:
49129ea
Reviewer: Frédéric Chapoton
Issue created by migration from https://trac.sagemath.org/ticket/34412
The text was updated successfully, but these errors were encountered: