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Invariants of solvable rigid Lie algebras up to dimension 8

Rutwig Campoamor-Stursberg, Fac Cc, Matemáticas U. C. M

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Abstract

The invariants of all complex solvable rigid Lie algebras up to dimension eight are computed. Moreover we show, for rank one solvable algebras, some criteria to deduce to non-existence of non-trivial invariants or the existence of fundamental sets of invariants formed by rational functions of the Casimir invariants of the associated nilradical. 1

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The invariants of all complex solvable rigid Lie algebras up to dimension eight are computed. Moreover we show, for rank one solvable algebras, some criteria to deduce to non-existence of non-trivial invariants or the existence of fundamental sets of invariants formed by rational functions of the Casimir invariants of the associated nilradical. 1

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Available abstract

The invariants of all complex solvable rigid Lie algebras up to dimension eight are computed. Moreover we show, for rank one solvable algebras, some criteria to deduce to non-existence of non-trivial invariants or the existence of fundamental sets of invariants formed by rational functions of the Casimir invariants of the associated nilradical. 1

Key concepts: Casimir effect, Mathematics, Dimension (graph theory), Pure mathematics, Rank (graph theory), Lie algebra, Algebra over a field, Combinatorics

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