Geometric characterisation of subvarieties of π6(π) related to the ternions and sextonions
- Author
- Anneleen De Schepper (UGent)
- Organization
- Project
- 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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8753227
- MLA
- De Schepper, Anneleen. βGeometric Characterisation of Subvarieties of π6(π) Related to the Ternions and Sextonions.β ADVANCES IN GEOMETRY, vol. 23, no. 1, 2022, pp. 69β106, doi:10.1515/advgeom-2022-0005.
- APA
- De Schepper, A. (2022). Geometric characterisation of subvarieties of π6(π) related to the ternions and sextonions. ADVANCES IN GEOMETRY, 23(1), 69β106. https://doi.org/10.1515/advgeom-2022-0005
- Chicago author-date
- De Schepper, Anneleen. 2022. βGeometric Characterisation of Subvarieties of π6(π) Related to the Ternions and Sextonions.β ADVANCES IN GEOMETRY 23 (1): 69β106. https://doi.org/10.1515/advgeom-2022-0005.
- Chicago author-date (all authors)
- De Schepper, Anneleen. 2022. βGeometric Characterisation of Subvarieties of π6(π) Related to the Ternions and Sextonions.β ADVANCES IN GEOMETRY 23 (1): 69β106. doi:10.1515/advgeom-2022-0005.
- Vancouver
- 1.De Schepper A. Geometric characterisation of subvarieties of π6(π) related to the ternions and sextonions. ADVANCES IN GEOMETRY. 2022;23(1):69β106.
- IEEE
- [1]A. De Schepper, βGeometric characterisation of subvarieties of π6(π) related to the ternions and sextonions,β ADVANCES IN GEOMETRY, vol. 23, no. 1, pp. 69β106, 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 π6(π) related to the ternions and sextonions}}, url = {{http://doi.org/10.1515/advgeom-2022-0005}}, volume = {{23}}, year = {{2022}}, }
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