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Lie algebras endowed with an action by automorphisms of the dicyclic group ofdegree 3 are considered. The close connections of these algebras with Liealgebras graded over the nonreduced root system BC1, with J-ternary algebrasand with Freudenthal-Kantor triple systems are explored.

Special Freudenthal–Kantor triple systems and Lie algebras with dicyclic symmetry