Implement faithful representations of nilpotent Lie algebras #37724
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mkoeppe
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Apr 5, 2024
mkoeppe
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Apr 5, 2024
mkoeppe
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Apr 5, 2024
mkoeppe
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mkoeppe
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mkoeppe
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mkoeppe
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Apr 5, 2024
mkoeppe
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Apr 5, 2024
src/sage/categories/finite_dimensional_lie_algebras_with_basis.py
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Last commit should address all of the comments. |
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Documentation preview for this PR (built with commit 643d320; changes) is ready! 🎉 |
mkoeppe
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Apr 10, 2024
| @@ -94,6 +97,44 @@ def _test_representation(self, **options): | |||
| for v in S: | |||
| tester.assertEqual(x.bracket(y) * v, x * (y * v) - y * (x * v)) | |||
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| def representation_matrix(self, elt): | |||
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The method of this name in sage.modules.with_basis.representation has additional keyword arguments, including side. Should this one too?
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No, the action is only implemented from the left. So it doesn't make sense to have it.
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sagemathgh-37779: Implementing the faithful representation of a generic Lie algebra in positive characteristic <!-- ^ Please provide a concise and informative title. --> <!-- ^ Don't put issue numbers in the title, do this in the PR description below. --> <!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method to calculate 1 + 2". --> <!-- v Describe your changes below in detail. --> <!-- v Why is this change required? What problem does it solve? --> <!-- v If this PR resolves an open issue, please link to it here. For example, "Fixes sagemath#12345". --> This is a very large representation in general, but it is known to be faithful. ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [x] I have created tests covering the changes. - [x] I have updated the documentation accordingly. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on. For example, --> <!-- - sagemath#12345: short description why this is a dependency --> <!-- - sagemath#34567: ... --> - sagemath#37724 Builds on this URL: sagemath#37779 Reported by: Travis Scrimshaw Reviewer(s): Matthias Köppe, Travis Scrimshaw
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We implement two methods to construct faithful representations of nilpotent Lie algebras. This is a first step towards implementing Ado's theorem.
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⌛ Dependencies