Free nilpotent Lie algebras

[ehaka]

Implement the construction of free nilpotent Lie algebras, i.e. Lie algebras where the only additional relations among the brackets are that iterated brackets longer than the nilpotency step must vanish.

Depends on #26074

CC: @tscrim

Component: algebra

Keywords: Lie algebras, nilpotent

Author: Eero Hakavuori

Branch/Commit: 664fbec

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/26076

[ehaka]

comment:1

Some implementation already exists in an external private codebase that I need to clean up and import into Sage.

[ehaka]

Commit: cb8a103

[ehaka]

Author: Eero Hakavuori

[ehaka]

comment:2

The adapted version of the free nilpotent Lie algebra construction is in the commits. I removed the parameter free from the method sage.algebras.lie_algebras.nilpotent_lie_algebra.NilpotentLieAlgebra of #26074, as the parameter seemed to be redundant.

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New commits:

19c27eb	New subcategories of Lie algebras (nilpotent, graded, stratified) and a base class for nilpotent Lie algebras
f58cddd	Implementation of the construction of free nilpotent Lie algebras
cb8a103	Changed doctests to use free nilpotent Lie algebras as more natural examples of graded or stratified Lie algebras

[ehaka]

Branch: u/gh-ehaka/free_nilpotent_lie_algebras-26076

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

158bfdb	Fix to product_space() for when L is not a true subalgebra of A.
293901e	Fixed a test for _test_generated_by_degree_one().
8658e9d	Fixing print order for fin-dim nilpotent Lie algebras with basis.
726639f	Some last little cleanup.
8b3c585	A better failure example for _test_generated_by_degree_one and some more doc.
a1e1ace	Refactored nilpotent Lie algebra constructor into Lie algebra constructor
14fcd30	Deduction rule for the fact that finite dimensional stratified Lie algebras are nilpotent
f1a0b1e	Docstring fix for indexing of grading of a stratification
4d4bdf6	Merge remote-tracking branch 'trac/public/lie_algebras/base_class_nilponent-26074' into free_nilpotent_lie_algebras
31fa53a	Added free nilpotent Lie algebras to LieAlgebra constructor

[sagetrac-git]

Changed commit from cb8a103 to 31fa53a

[sagetrac-git]

Changed commit from 31fa53a to b7c8a2a

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a3dccfd	Merge branch 'public/lie_algebras/base_class_nilponent-26074' of git://trac.sagemath.org/sage into public/lie_algebras/base_class_nilponent-26074
0fa41ad	Fixing doctests, making category an arugment, and other small tweaks.
53a10be	Adding an extra doctest and fix for the category option.
d7077cd	Merge remote-tracking branch 'trac/public/lie_algebras/base_class_nilponent-26074' into u/gh-ehaka/free_nilpotent_lie_algebras-26076
b7c8a2a	Fixed category parameter of initialization of free nilpotent Lie algebra

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

a5ec3ad	Moving the axioms around for better printing.
09b54f5	Merge remote-tracking branch 'trac/public/lie_algebras/base_class_nilponent-26074' into u/gh-ehaka/free_nilpotent_lie_algebras-26076