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arXiv 2001.033952020-01-13math.COmath.RA

Veronese representation of projective Hjelmslev planes over some quadratic alternative algebras

Anneleen De Schepper, Hendrik Van Maldeghem

备注：: 51 pages
发表信息：: Results Math (2020) 75:9
DOI：: 10.1007/s00025-019-1133-5

英文摘要：

We geometrically characterise the Veronese representations of ring projective planes over algebras which are analogues of the dual numbers, giving rise to projective Hjelmslev planes of level 2 coordinatised over quadratic alternative algebras. These planes are related to affine buildings of relative type $\widetilde{A}_2$ and respective absolute type $\widetilde{\mathsf{A}}_2$, $\widetilde{\mathsf{A}}_5$ and $\widetilde{\mathsf{E}}_6$.

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