Inner ideals and structurable algebras : Moufang sets, triangles and hexagons
- Author
- Tom De Medts (UGent) and Jeroen Meulewaeter
- Organization
- Project
- Abstract
- We construct Moufang sets, Moufang triangles and Moufang hexagons using inner ideals of Lie algebras obtained from structurable algebras via the Tits-Kantor-Koecher construction. The three different types of structurable algebras we use are, respectively: (1) structurable division algebras, (2) algebras D & OPLUS; D for some alternative division algebra D, equipped with the exchange involution, (3) matrix structurable algebras M (J, 1) for some cubic Jordan division algebra J. In each case, we also determine the root groups directly in terms of the structurable algebra.
- Keywords
- General Mathematics, LIE-ALGEBRAS, QUADRANGLES, IDENTITIES, ELEMENTS, E-6
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01HQ0YD4T55NBHGD94JYXXG50R
- MLA
- De Medts, Tom, and Jeroen Meulewaeter. “Inner Ideals and Structurable Algebras : Moufang Sets, Triangles and Hexagons.” ISRAEL JOURNAL OF MATHEMATICS, vol. 259, no. 1, 2024, pp. 33–88, doi:10.1007/s11856-023-2491-y.
- APA
- De Medts, T., & Meulewaeter, J. (2024). Inner ideals and structurable algebras : Moufang sets, triangles and hexagons. ISRAEL JOURNAL OF MATHEMATICS, 259(1), 33–88. https://doi.org/10.1007/s11856-023-2491-y
- Chicago author-date
- De Medts, Tom, and Jeroen Meulewaeter. 2024. “Inner Ideals and Structurable Algebras : Moufang Sets, Triangles and Hexagons.” ISRAEL JOURNAL OF MATHEMATICS 259 (1): 33–88. https://doi.org/10.1007/s11856-023-2491-y.
- Chicago author-date (all authors)
- De Medts, Tom, and Jeroen Meulewaeter. 2024. “Inner Ideals and Structurable Algebras : Moufang Sets, Triangles and Hexagons.” ISRAEL JOURNAL OF MATHEMATICS 259 (1): 33–88. doi:10.1007/s11856-023-2491-y.
- Vancouver
- 1.De Medts T, Meulewaeter J. Inner ideals and structurable algebras : Moufang sets, triangles and hexagons. ISRAEL JOURNAL OF MATHEMATICS. 2024;259(1):33–88.
- IEEE
- [1]T. De Medts and J. Meulewaeter, “Inner ideals and structurable algebras : Moufang sets, triangles and hexagons,” ISRAEL JOURNAL OF MATHEMATICS, vol. 259, no. 1, pp. 33–88, 2024.
@article{01HQ0YD4T55NBHGD94JYXXG50R,
abstract = {{We construct Moufang sets, Moufang triangles and Moufang hexagons using inner ideals of Lie algebras obtained from structurable algebras via the Tits-Kantor-Koecher construction. The three different types of structurable algebras we use are, respectively: (1) structurable division algebras, (2) algebras D & OPLUS; D for some alternative division algebra D, equipped with the exchange involution, (3) matrix structurable algebras M (J, 1) for some cubic Jordan division algebra J. In each case, we also determine the root groups directly in terms of the structurable algebra.}},
author = {{De Medts, Tom and Meulewaeter, Jeroen}},
issn = {{0021-2172}},
journal = {{ISRAEL JOURNAL OF MATHEMATICS}},
keywords = {{General Mathematics,LIE-ALGEBRAS,QUADRANGLES,IDENTITIES,ELEMENTS,E-6}},
language = {{eng}},
number = {{1}},
pages = {{33--88}},
title = {{Inner ideals and structurable algebras : Moufang sets, triangles and hexagons}},
url = {{http://doi.org/10.1007/s11856-023-2491-y}},
volume = {{259}},
year = {{2024}},
}
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