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Computation of invariants of Lie algebras by means of moving frames. (English) Zbl 1106.17040
Summary: A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of Lie algebras. It uses the Cartan method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. The algorithm is applied, in particular, to computation of invariants of real low-dimensional Lie algebras. A number of examples are calculated to illustrate its effectiveness and to make a comparison with the same cases in the literature. Bases of invariants of the real six-dimensional solvable Lie algebras with four-dimensional nilradicals are newly calculated and listed in a table.

17B81Applications of Lie algebras to physics
17B30Solvable, nilpotent Lie (super)algebras
81R05Representations of finite-dimensional groups and algebras in quantum theory
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