[Sage] #14901: Lie algebras

[Sage]

#14901: Lie algebras
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.12
Component: algebra | Keywords: Lie algebras Kac Moody
Work issues: | Report Upstream: N/A
Reviewers: | Authors: Travis Scrimshaw
Merged in: | Dependencies: #10963
Stopgaps: |
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Initial implementation of Lie algebras in sage.

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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14901>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, and MATLAB

[Sage]

#14901: Lie algebras
------------------------------------------+---------------------------------

Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.12

Component: algebra | Resolution:

Keywords: Lie algebras Kac Moody | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Travis Scrimshaw | Merged in:
Dependencies: #10963 | Stopgaps:

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Description changed by tscrim:

Old description:

> Initial implementation of Lie algebras in sage.

New description:

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 + 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).

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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14901#comment:1>