Generalised Killing Spinors on Three-Dimensional Lie Groups

Abstract

We present a complete classification of invariant generalised Killing spinors on three-dimensional Lie groups. We show that, in this context, the existence of a non-trivial invariant generalised Killing spinor implies that all invariant spinors are generalised Killing with the same endomorphism. Notably, this classification is independent of the choice of left-invariant metric. To illustrate the computational methods underlying this classification, we also provide the first known examples of homogeneous manifolds admitting invariant generalised Killing spinors with $n$ distinct eigenvalues for each $n>4$.

arXiv commentTo appear in Manuscripta Mathematica. Incorporated suggestions from anonymous referees

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Cited by in corpus (1)

• Invariant Spinors on Flag Manifolds