Equivalent conditions on the structure equations of 3D Lie algebras determine which left-invariant pseudo-Riemannian metrics admit left-invariant harmonic spinors.
Freibert,Cocalibrated structures on Lie algebras with a codimension one Abelian ideal
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Left-invariant harmonic spinors on three-dimensional Lie groups
Equivalent conditions on the structure equations of 3D Lie algebras determine which left-invariant pseudo-Riemannian metrics admit left-invariant harmonic spinors.