Opened 9 years ago
Last modified 2 months ago
#14901 new task
Lie algebras — at Version 4
Reported by: | tscrim | Owned by: | sage-combinat |
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Priority: | major | Milestone: | sage-feature |
Component: | algebra | Keywords: | Lie algebras, Kac Moody, days54, fpsac2019 |
Cc: | sage-combinat, aschilling, nthiery, darij, bsalisbury1, bump, SimonKing | Merged in: | |
Authors: | Travis Scrimshaw | Reviewers: | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | #10963 | Stopgaps: |
Description (last modified by )
Initial implementation of Lie algebras in sage.
This will contain the following:
- Free Lie algebras in the Hall basis
- Abelian Lie algebras
- Lie algebras from an associative algebra
- Lie algebras from structure coefficients
- Finite type Lie algebras
- As matrices for types ABCD
- In the Chevalley basis
- gl_{n}
- The Lie algebra of strictly upper triangular matrices
- The Lie algebra of upper triangular matrices
- Untwisted affine Lie algebras constructed from a finite type
- Untwisted affine Kac-Moody Lie algebras (i.e. the above and the Lie derivative)
- Universal enveloping algebras
There might also be the following:
- The Lyndon basis for the free Lie algebra
- su_{n}
- Kac-Moody algebras based only on a (generalized) Cartan matrix
With this, one will be able to do basic computations, as well as compute things such as the lower central series (depending on the type).
Change History (4)
comment:1 Changed 9 years ago by
- Description modified (diff)
comment:2 Changed 9 years ago by
- Cc darij added
comment:3 Changed 9 years ago by
- Cc bsalisbury1 added
comment:4 Changed 9 years ago by
- Description modified (diff)
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