Journal of Lie Theory

The index of nilpotent Lie algebras
Burde, Dietrich1 orcid ; Dekimpe, Karel2 orcid
1Fakultät für Mathematik, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
2Katholieke Universiteit Leuven Campus Kulak Kortrijk, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium
Journal of Lie Theory, Online first, pp. 1-17

The index of a Lie algebra is an important invariant which arises in several areas, e.g. in the study of coadjoint orbits for a Lie group, in invariant theory and in representation theory. We study the index for several classes of nilpotent Lie algebras. In particular, we give explicit formulas for free-nilpotent Lie algebras of nilpotency class two and three, or of solvability class two, for graph Lie algebras, and for filiform nilpotent Lie algebras.

Received:
Accepted:
DOI: 10.5802/jolt.1435
Classification: 17B30, 17B08
Keywords: index, Lie algebra

Burde, Dietrich  1 ; Dekimpe, Karel  2

1 Fakultät für Mathematik, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
2 Katholieke Universiteit Leuven Campus Kulak Kortrijk, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium 
Burde, Dietrich; Dekimpe, Karel. The index of nilpotent Lie algebras. Journal of Lie Theory, Online first, pp. 1-17
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