Involutive moving frames II; The Lie-Tresse theorem |
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Institution: | Department of Mathematics, University of Iceland, Reykjavík, Ssn. 600169-2039, Iceland |
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Abstract: | This paper continues the project, begun in 1], of harmonizing Cartan's classical equivalence method and the modern equivariant moving frame in a framework dubbed involutive moving frames. As an attestation of the fruitfulness of our framework, we obtain a new, constructive and intuitive proof of the Lie-Tresse theorem (Fundamental basis theorem) and a first general upper bound on the minimal number of generating differential invariants for Lie pseudo-groups. Further, we demonstrate the computational advantages of this framework by studying the equivalence problem for first order PDE in two independent variables and one dependent variable under point transformations. |
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Keywords: | Moving frames Equivalence problems Differential invariants |
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