Geometric characterisation of subvarieties of 𝓔<sub>6</sub>(𝕂) related to the ternions and sextonions-Reference-Cited by-同舟云学术

Geometric characterisation of subvarieties of 𝓔₆(𝕂) related to the ternions and sextonions

Published:2022-04-18 Issue:1 Volume:23 Page:69-106
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

De Schepper Anneleen¹

Affiliation:

1. Department of Mathematics: Algebra and Geometry , Ghent University , Krijgslaan , 281-S25, 9000 Ghent , Belgium

Abstract

Abstract The main achievement of this paper is a geometric characterisation of certain subvarieties of the Cartan variety 𝓔6(𝕂) over an arbitrary field 𝕂. The characterised varieties arise as Veronese representations of certain ring projective planes over quadratic subalgebras of the split octonions 𝕆’ over 𝕂 (among which the sextonions, a 6-dimensional non-associative algebra). We describe how these varieties are linked to the Freudenthal–Tits magic square, and discuss how they would even fit in, when also allowing the sextonions and other “degenerate composition algebras” as the algebras used to construct the square.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2022-0005/pdf

Reference18 articles.

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3. A. De Schepper, J. Schillewaert, H. Van Maldeghem, A uniform characterisation of the varieties of the second row of the Freudenthal–Tits Magic Square over arbitrary fields. Submitted. https://cage.ugent.be/$~$ads/links/8.pdf

4. A. De Schepper, J. Schillewaert, H. Van Maldeghem, M. Victoor, Constructions and characterisation of the varieties of the third row of the Freudenthal–Tits Magic Square. In progress.

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