Opened 2 years ago

Closed 2 years ago

# Implement universal commutative algebra of a finite-dimensional Lie algebra

Reported by: Owned by: Travis Scrimshaw major sage-9.2 algebra Travis Scrimshaw Reimundo Heluani N/A a1ea948 a1ea948d7858e2e6d004ec898fd5dbcaf5e92791

### Description

This was defined recently in arXiv:2006.00711.

### comment:1 Changed 2 years ago by Travis Scrimshaw

Branch: → public/lie_algebras/universal_commutative_algebra-30236 → b99e452a216cda039dabae4a466aa5851c193c00 new → needs_review

New commits:

 ​b99e452 Implement universal commutative algebra of a Lie algebra.

### comment:2 Changed 2 years ago by Reimundo Heluani

Just in case you haven't changed it yet, in line five of the docstring for universal_polynomials it should read:

[e_i, e_j] = \tau_{ij}^a e_a is given by

It's missing the second `

### comment:3 Changed 2 years ago by Reimundo Heluani

Also, the definition in the docstring does not seem to coincide with equation (6) in the reference. In the paper https://arxiv.org/pdf/2006.00711.pdf the definition of the universal polynomials in this case is

P_{aij} = \sum_{u \in I} \tau_{ij}^u X_{au}
- \sum_{s,t \in I} \tau_{st}^a X_{si} X_{tj},

as opposed to the current:

P_{aij} = \sum_{u \in I} \tau_{ij}^u X_{au}
- \sum_{s,t \in I} \tau_{st}^a X_{ai} X_{tj},

### comment:4 Changed 2 years ago by Reimundo Heluani

The issue in comment:3 is only a typo in the docstring, the code seems fine.

Finally, don't you have a problem reading your variables if the dimension of the Lie algebra is >10?

The rest looks good to me.

### comment:5 Changed 2 years ago by git

Commit: b99e452a216cda039dabae4a466aa5851c193c00 → a1ea948d7858e2e6d004ec898fd5dbcaf5e92791

Branch pushed to git repo; I updated commit sha1. New commits:

 ​2e53d37 Merge branch 'public/lie_algebras/universal_commutative_algebra-30236' of git://trac.sagemath.org/sage into public/lie_algebras/universal_commutative_algebra-30236 ​a1ea948 Addressing reviewer comments. Handling dim >= 10.

### comment:6 Changed 2 years ago by Travis Scrimshaw

Good point about the variable names. I have fixed this and the other two typos.

### comment:7 follow-up:  8 Changed 2 years ago by Reimundo Heluani

ran it in my bot and came back green, I don't know why you would want different naming schemes for Lie algebras of different dimensions, but either way this looks fine to me. If I'm allowed to be a reviewer you can put a positive review on my behalf.

### comment:8 in reply to:  7 Changed 2 years ago by Travis Scrimshaw

ran it in my bot and came back green, I don't know why you would want different naming schemes for Lie algebras of different dimensions, but either way this looks fine to me.

I want the more compact version for the variables when the dimension is small. The larger dimensions was just to remove the ambiguity.

If I'm allowed to be a reviewer you can put a positive review on my behalf.

Yes you most certainly are. Just put in your full name as the reviewer and you can set the positive review.

### comment:9 Changed 2 years ago by Reimundo Heluani

Reviewers: → Reimundo Heluani needs_review → positive_review

Thank you.

### comment:11 Changed 2 years ago by Volker Braun

Branch: public/lie_algebras/universal_commutative_algebra-30236 → a1ea948d7858e2e6d004ec898fd5dbcaf5e92791 → fixed positive_review → closed
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