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- Title
Lie Invariants in Two and Three Variables.
- Authors
Bremner, Murray R.; Hu, Jiaxiong
- Abstract
We use computer algebra to determine the Lie invariants of degree ≤ 12 in the free Lie algebra on two generators corresponding to the natural representation of the simple 3-dimensional Lie algebra 픰픩2(ℂ). We then consider the free Lie algebra on three generators, and compute the Lie invariants of degree ≤ 7 corresponding to the adjoint representation of 픰픩2(ℂ), and the Lie invariants of degree ≤ 9 corresponding to the natural representation of 픰픩3(ℂ). We represent the action of 픰픩2(ℂ) and 픰픩3(ℂ) on Lie polynomials by computing the coefficient matrix with respect to the basis of Hall words.
- Subjects
INVARIANTS (Mathematics); ALGEBRA software; GENERATORS (Computer programs); REPRESENTATION theory; HERMITE polynomials; ALGORITHMS
- Publication
Algebra Colloquium, 2014, Vol 21, Issue 1, p95
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386714000078