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arXiv · 2401.04548

Generalised Killing Spinors on Three-Dimensional Lie Groups

Diego Artacho
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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 $n > 4$.

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Diego Artacho. 2024-01-09. Generalised Killing Spinors on Three-Dimensional Lie Groups. https://doi.org/10.1007/s00229-025-01617-y

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