Abstract
Over the field of one element, vector bundles over n-dimensional projective spaces are considered. It is shown that all line bundles are tensor powers of the Hopf bundle and all vector bundles are direct sums of line bundles. This is in complete analogy to the case of the projective line over an arbitrary classical field, but drastically simpler in comparison with projective spaces of higher dimensions.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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von Bothmer, HC.G., Hinsch, L. & Stuhler, U. Vector bundles over projective spaces. The case \({\mathbb F_1}\) . Arch. Math. 96, 227–234 (2011). https://doi.org/10.1007/s00013-011-0225-6
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DOI: https://doi.org/10.1007/s00013-011-0225-6