Abstract:We use elementary linear algebra to explicitly calculate a basis for, and the dimension of, the space of degree-three covariants for a binary form of arbitrary degree. We also give an explicit basis for the subspace of covariants complementary to the space of degree-three reducible covariants. The study of invariant functions was one of the main influences on the development of modern algebra. Consider the following simple example. The group G = ޚ acts on ޒ by addition: g • x = g + x. We define a G-invaria… Show more
“…Λ where all arrows are sl 2 -homomorphisms, and Λ Λ(P(S)) = S. Thus Λ is a surjective map. The part of theorem concerning ker Λ • χ can be proved in the same manner as the proof in the preprint [10], see also [12].…”
A method based on the symbolic methods of the classical invariant theory is developed for a representation of elements of kernel of Weitzenbök derivations.
“…Λ where all arrows are sl 2 -homomorphisms, and Λ Λ(P(S)) = S. Thus Λ is a surjective map. The part of theorem concerning ker Λ • χ can be proved in the same manner as the proof in the preprint [10], see also [12].…”
A method based on the symbolic methods of the classical invariant theory is developed for a representation of elements of kernel of Weitzenbök derivations.
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