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Implement twisted affine Lie algebras #35591

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merged 5 commits into from
May 28, 2023

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tscrim
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@tscrim tscrim commented May 1, 2023

📚 Description

Untwisted affine Lie algebras have been implemented in Sage for some time, but their twisted counterparts have been missing. They are more complicated to implement due to the involvement of a diagram automorphism, third roots of unity, and nonreduced root systems.

Along the way, I made some additional fixes in regards to this enhancement:

  • Brings coverage up to 100% in lie_algebras.
  • Faster Killing matrix for Chevalley basis (which speeds up untwisted affine brackets).
  • Fix bug in creating the affine type from a finite type.

📝 Checklist

  • The title is concise, informative, and self-explanatory.
  • The description explains in detail what this PR is about.
  • I have linked a relevant issue or discussion.
  • I have created tests covering the changes.
  • I have updated the documentation accordingly.

⌛ Dependencies

…vements.

- Brings coverage up to 100% in lie_algebras.
- Faster Killing matrix for Chevalley basis (which speeds up untwisted
  affine brackets).
- Fix bug in creating the affine type from a finite type.
@fchapoton
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linter not happy and doctest failing

@tscrim tscrim force-pushed the lie_algebras/twisted_affine branch from a4198ba to f50a218 Compare May 2, 2023 14:37
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tscrim commented May 2, 2023

This should make it pass the tests; I forgot to add in the output. I also fixed the docbuild issue (although shortening a 3 letter name to 2 letters for a reference is a bit strange to me...). I also did the changes the linter is requiring, but IMO it makes the code less readable (I really don't see any utility of that blankline before nested definitions and only to those (not, e.g., for if statements too)).

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There are still some Kac1990 so the doc does not build

@tscrim tscrim force-pushed the lie_algebras/twisted_affine branch from a3798ed to 27593ea Compare May 2, 2023 22:57
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tscrim commented May 2, 2023

Right, sorry about that. I didn't grep carefully enough.

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Documentation preview for this PR (built with commit fd069d7) is ready! 🎉

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ok, let it be

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tscrim commented May 27, 2023

Thank you.

@vbraun vbraun merged commit a105ea6 into sagemath:develop May 28, 2023
@mkoeppe mkoeppe added this to the sage-10.1 milestone May 28, 2023
@tscrim tscrim deleted the lie_algebras/twisted_affine branch May 29, 2023 00:20
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4 participants