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 c...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.展开更多
文摘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.
