arXiv 2203.026712022-03-05math.RAhep-thmath-phmath.MP

Octonionic Planes and Real Forms of G2, F4 and E6

Daniele Corradetti, Alessio Marrani, David Chester, Raymond Aschheim

备注：: 16 pages, 3 figures
DOI：: 10.7546/giq-23-2022-39-57

英文摘要：

In this work we present a useful way to introduce the octonionic projective and hyperbolic plane through the use of Veronese vectors. Then we focus on their relation with the exceptional Jordan algebra and show that the Veronese vectors are the rank-one elements of the algebra. We then study groups of motions over the octonionic plane recovering all real forms of G2, F4and E6 groups and finally give a classification of all octonionic and split-octonionic planes as symmetric spaces.

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