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

(2022) ADVANCES IN GEOMETRY. 23(1). p.69-106
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Abstract
The main achievement of this paper is a geometric characterisation of certain subvarieties of the Cartan variety E_6(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.
Keywords
Veronese varieties, ring geometries, composition algebras, Freudenthal-Tits magic square, E6

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MLA
De Schepper, Anneleen. β€œGeometric Characterisation of Subvarieties of 𝓔6(𝕂) Related to the Ternions and Sextonions.” ADVANCES IN GEOMETRY, vol. 23, no. 1, 2022, pp. 69–106, doi:10.1515/advgeom-2022-0005.
APA
De Schepper, A. (2022). Geometric characterisation of subvarieties of 𝓔6(𝕂) related to the ternions and sextonions. ADVANCES IN GEOMETRY, 23(1), 69–106. https://doi.org/10.1515/advgeom-2022-0005
Chicago author-date
De Schepper, Anneleen. 2022. β€œGeometric Characterisation of Subvarieties of 𝓔6(𝕂) Related to the Ternions and Sextonions.” ADVANCES IN GEOMETRY 23 (1): 69–106. https://doi.org/10.1515/advgeom-2022-0005.
Chicago author-date (all authors)
De Schepper, Anneleen. 2022. β€œGeometric Characterisation of Subvarieties of 𝓔6(𝕂) Related to the Ternions and Sextonions.” ADVANCES IN GEOMETRY 23 (1): 69–106. doi:10.1515/advgeom-2022-0005.
Vancouver
1.
De Schepper A. Geometric characterisation of subvarieties of 𝓔6(𝕂) related to the ternions and sextonions. ADVANCES IN GEOMETRY. 2022;23(1):69–106.
IEEE
[1]
A. De Schepper, β€œGeometric characterisation of subvarieties of 𝓔6(𝕂) related to the ternions and sextonions,” ADVANCES IN GEOMETRY, vol. 23, no. 1, pp. 69–106, 2022.
@article{8753227,
  abstract     = {{The main achievement of this paper is a geometric characterisation of certain subvarieties of the Cartan variety E_6(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.}},
  author       = {{De Schepper, Anneleen}},
  issn         = {{1615-715X}},
  journal      = {{ADVANCES IN GEOMETRY}},
  keywords     = {{Veronese varieties,ring geometries,composition algebras,Freudenthal-Tits magic square,E6}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{69--106}},
  title        = {{Geometric characterisation of subvarieties of 𝓔6(𝕂) related to the ternions and sextonions}},
  url          = {{http://dx.doi.org/10.1515/advgeom-2022-0005}},
  volume       = {{23}},
  year         = {{2022}},
}

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