Centerless unimodular DS-contact Lie algebras are only sl(2,R) and su(2), with the Reeb vector's adjoint action nilpotent except in these cases.
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On centerless unimodular contact Lie algebras
Centerless unimodular DS-contact Lie algebras are only sl(2,R) and su(2), with the Reeb vector's adjoint action nilpotent except in these cases.