Lie Invariants in Two and Three Variables
نویسنده
چکیده
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 sl2(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 sl2(C), and the Lie invariants of degree ≤ 9 corresponding to the natural representation of sl3(C). We represent the action of sl2(C) and sl3(C) on Lie polynomials by computing the coefficient matrix with respect to the basis of Hall words. We then use algorithms for linear algebra (row canonical form, Hermite normal form, lattice basis reduction) to compute a basis of the nullspace.
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