We define a new invariant of quadratic Lie algebras and give a complete study and classification of singular quadratic Lie
algebras, i.e. those for which the invariant does not vanish. The classification is related to O(
n)-adjoint orbits in
\mathfrako(n)\mathfrak{o}(n).
Keywords Quadratic Lie algebras – Invariants – Double extensions – Adjoint orbits – Solvable Lie algebras
Mathematics Subject Classifications (2010) 17B05 – 17B20 – 17B30
Presented by Rudolf Rentschler.