Spin spaces, Lipschitz groups, and spinor bundles
| dc.creator | Friedrich, Thomas | |
| dc.creator | Trautman, Andrzej | |
| dc.date | 1999-01-29 | |
| dc.date.accessioned | 2026-07-07T05:27:42Z | |
| dc.date.available | 2026-07-07T05:27:42Z | |
| dc.description | It is shown that every bundle $\varSigma\to M$ of complex spinor modules over the Clifford bundle $\Cl(g)$ of a Riemannian space $(M,g)$ with local model $(V,h)$ is associated with an lpin ("Lipschitz") structure on $M$, this being a reduction of the ${\Ort}(h)$-bundle of all orthonormal frames on M to the Lipschitz group $\Lpin(h)$ of all automorphisms of a suitably defined spin space. An explicit construction is given of the total space of the $\Lpin(h)$-bundle defining such a structure. If the dimension m of M is even, then the Lipschitz group coincides with the complex Clifford group and the lpin structure can be reduced to a pin$^{c}$ structure. If m=2n-1, then a spinor module $\varSigma$ on M is of the Cartan type: its fibres are 2^n-dimensional and decomposable at every point of M, but the homomorphism of bundles of algebras $\Cl(g)\to\End\varSigma$ globally decomposes if, and only if, M is orientable. Examples of such bundles are given. The topological condition for the existence of an lpin structure on an odd-dimensional Riemannian manifold is derived and illustrated by the example of a manifold admitting such a structure, but no pin^c structure. | |
| dc.description | Latex2.09, 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/9901137 | |
| dc.identifier | http://arxiv.org/abs/math/9901137 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78018 | |
| dc.subject | Differential Geometry | |
| dc.subject | Primary 15A66 and 53A50; Secondary 81R25 and 83C60 | |
| dc.title | Spin spaces, Lipschitz groups, and spinor bundles | |
| dc.type | text |