Opened 2 years ago

Closed 2 years ago

## #30236 closed enhancement (fixed)

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

Reported by: | Travis Scrimshaw | Owned by: | |
---|---|---|---|

Priority: | major | Milestone: | sage-9.2 |

Component: | algebra | Keywords: | |

Cc: | Merged in: | ||

Authors: | Travis Scrimshaw | Reviewers: | Reimundo Heluani |

Report Upstream: | N/A | Work issues: | |

Branch: | a1ea948 (Commits, GitHub, GitLab) | Commit: | a1ea948d7858e2e6d004ec898fd5dbcaf5e92791 |

Dependencies: | Stopgaps: |

### Description

This was defined recently in arXiv:2006.00711.

### Change History (11)

### comment:1 Changed 2 years ago by

Branch: | → public/lie_algebras/universal_commutative_algebra-30236 |
---|---|

Commit: | → b99e452a216cda039dabae4a466aa5851c193c00 |

Status: | new → needs_review |

### comment:2 Changed 2 years ago by

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

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

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

Commit: | b99e452a216cda039dabae4a466aa5851c193c00 → a1ea948d7858e2e6d004ec898fd5dbcaf5e92791 |
---|

### comment:6 Changed 2 years ago by

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

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 Changed 2 years ago by

Replying to 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.

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

Reviewers: | → Reimundo Heluani |
---|---|

Status: | needs_review → positive_review |

### comment:11 Changed 2 years ago by

Branch: | public/lie_algebras/universal_commutative_algebra-30236 → a1ea948d7858e2e6d004ec898fd5dbcaf5e92791 |
---|---|

Resolution: | → fixed |

Status: | positive_review → closed |

**Note:**See TracTickets for help on using tickets.

New commits:

`Implement universal commutative algebra of a Lie algebra.`