Computation of Invariants of Lie Algebras by Means of Moving Frames

Abstract

A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of Lie algebras. It uses the Cartan's 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 solvable Lie algebras up to dimension five, the real six-dimensional nilpotent Lie algebras and the real six-dimensional solvable Lie algebras with four-dimensional nilradicals are newly calculated and listed in tables.

17 pages, extended version

References in corpus (4)

• A class of solvable Lie algebras and their Casimir Invariants
• Invariants of Lie Algebras with Fixed Structure of Nilradicals
• Invariants of the nilpotent and solvable triangular Lie algebras
• Invariants of a semi-direct sum of Lie algebras

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