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- Title
Geometric characterisation of subvarieties of 퓔<sub>6</sub>(핂) related to the ternions and sextonions.
- Authors
De Schepper, Anneleen
- Abstract
The main achievement of this paper is a geometric characterisation of certain subvarieties of the Cartan variety 퓔6(핂) over an arbitrary field 핂. The characterised varieties arise as Veronese representations of certain ring projective planes over quadratic subalgebras of the split octonions 핆' over 핂 (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.
- Subjects
NONASSOCIATIVE algebras; CAYLEY numbers (Algebra); ALGEBRA; MAGIC squares; ASSOCIATIVE rings
- Publication
Advances in Geometry, 2023, Vol 23, Issue 1, p69
- ISSN
1615-715X
- Publication type
Article
- DOI
10.1515/advgeom-2022-0005