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Keywords:
geometry of ordinary differential equations; normal Cartan connections, cohomology of Lie algebras
geometry of ordinary differential equations; normal Cartan connections, cohomology of Lie algebras
Summary:
We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of semisimple Lie algebras. We compute differential invariants up to degree 2 as application.
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