Generalised Killing Spinors on Three-Dimensional Lie Groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929702780796928 |
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| author | Artacho, Diego |
| author_facet | Artacho, Diego |
| contents | 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 $n > 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalised Killing Spinors on Three-Dimensional Lie Groups Artacho, Diego Differential Geometry Representation Theory 53C27 (Primary), 22E60, 15A66 (Secondary) 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 $n > 4$. |
| title | Generalised Killing Spinors on Three-Dimensional Lie Groups |
| topic | Differential Geometry Representation Theory 53C27 (Primary), 22E60, 15A66 (Secondary) |
| url | https://arxiv.org/abs/2401.04548 |