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Kantor Triple Systems

Mondoc, Daniel LU (2002) In Doctoral theses in mathematical sciences 2002(9).
Abstract
The main purpose of this thesis is to study real exceptional Kantor triple systems. In the first paper we first prove the known results in both the real and complex classical cases of K-simple Kantor triple systems. In the real classical case our approach gives somewhat simpler formulas. Special attention is given to all real classical cases of K-simple Kantor triple systems that can be presented in another isomorphic form, i.e. defined on tensor products of composition algebras. They are of interest in their own right and help to understand the real exceptional case. Then we consider the real exceptional K-simple Kantor triple systems. The main result of the first paper is the classification up to weak isomorphism of all real exceptional... (More)
The main purpose of this thesis is to study real exceptional Kantor triple systems. In the first paper we first prove the known results in both the real and complex classical cases of K-simple Kantor triple systems. In the real classical case our approach gives somewhat simpler formulas. Special attention is given to all real classical cases of K-simple Kantor triple systems that can be presented in another isomorphic form, i.e. defined on tensor products of composition algebras. They are of interest in their own right and help to understand the real exceptional case. Then we consider the real exceptional K-simple Kantor triple systems. The main result of the first paper is the classification up to weak isomorphism of all real exceptional K-simple Kantor triple systems defined on tensor products of composition algebras. Also, a description of the split and the five remaining cases is given. In the second paper we develop the main result of the first paper and give a classification up to isomorphism of real simple compact Kantor triple systems defined on tensor products of composition algebras. The classification is given by presenting a unified formula for multiplication in these triples. In addition, we obtain an explicit formula for the canonical trace form for real simple compact Kantor triple systems defined on tensor products of composition algebras. (Less)
Abstract (Swedish)
Popular Abstract in Swedish

Avhandlingens huvudsyfte är att studera reella exceptionella Kantortrippelsystem. I första artikeln visar vi först kända resultat i både de reella och komplexa klassiska fallen av K-enkla Kantortrippelsystem. I de reella klassiska fallen ger vår lösning enklare formler. Speciell uppmärksamhet ges till de reella klassiska fallen som är definierade på tensorprodukter av algebror av hyperkomplexa tal. De är av intresse i sig själva och hjälper förståelsen för de reella exceptionella fallen som vi betraktar därefter. Första artikelns huvudresultat är klassificeringen upp till svag isomorfism av alla reella exceptionella K-enkla Kantortrippelsystem definierade på tensorprodukter av algebror av... (More)
Popular Abstract in Swedish

Avhandlingens huvudsyfte är att studera reella exceptionella Kantortrippelsystem. I första artikeln visar vi först kända resultat i både de reella och komplexa klassiska fallen av K-enkla Kantortrippelsystem. I de reella klassiska fallen ger vår lösning enklare formler. Speciell uppmärksamhet ges till de reella klassiska fallen som är definierade på tensorprodukter av algebror av hyperkomplexa tal. De är av intresse i sig själva och hjälper förståelsen för de reella exceptionella fallen som vi betraktar därefter. Första artikelns huvudresultat är klassificeringen upp till svag isomorfism av alla reella exceptionella K-enkla Kantortrippelsystem definierade på tensorprodukter av algebror av hyperkomplexa tal. Vi ger också en beskrivning av ''splitfallen'' och de fem återstående fallen. I det andra artikeln utveklar vi första artikelns huvudresultat och ger klassificeringen upp till isomorphism av alla reella enkla kompakta Kantortrippelsystem definierade på tensorprodukter av algebror av hyperkomplexa tal. Klassificeringen ges av en enhetlig formel för multiplikationen i dessa trippelsystem. Vi ger också en explicit formel för den kanoniska spårformen för reella enkla kompakta Kantortrippelsystem definierade på tensorprodukter av algebror av hyperkomplexa tal. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • ass. Prof Mazorchuk, Volodymyr, Uppsala Univ., Uppsala, SWEDEN
organization
publishing date
type
Thesis
publication status
published
subject
keywords
gruppteori, fältteori, algebra, algebraic geometry, group theory, Talteori, field theory, Number Theory, Composition algebras, Jordan algebras, Kantor triple systems, Lie algebras, Jordan triple systems, algebraisk geometri
in
Doctoral theses in mathematical sciences
volume
2002
issue
9
pages
169 pages
publisher
Centre for the Mathematical sciences, Lund University
defense location
MH:C
defense date
2003-02-10 10:15:00
ISSN
1404-0034
ISBN
91-628-5513-1
language
English
LU publication?
yes
id
61207464-6a36-4d53-920c-2d2f84bf1983 (old id 465393)
date added to LUP
2016-04-01 16:13:40
date last changed
2020-05-28 10:38:13
@phdthesis{61207464-6a36-4d53-920c-2d2f84bf1983,
  abstract     = {The main purpose of this thesis is to study real exceptional Kantor triple systems. In the first paper we first prove the known results in both the real and complex classical cases of K-simple Kantor triple systems. In the real classical case our approach gives somewhat simpler formulas. Special attention is given to all real classical cases of K-simple Kantor triple systems that can be presented in another isomorphic form, i.e. defined on tensor products of composition algebras. They are of interest in their own right and help to understand the real exceptional case. Then we consider the real exceptional K-simple Kantor triple systems. The main result of the first paper is the classification up to weak isomorphism of all real exceptional K-simple Kantor triple systems defined on tensor products of composition algebras. Also, a description of the split and the five remaining cases is given. In the second paper we develop the main result of the first paper and give a classification up to isomorphism of real simple compact Kantor triple systems defined on tensor products of composition algebras. The classification is given by presenting a unified formula for multiplication in these triples. In addition, we obtain an explicit formula for the canonical trace form for real simple compact Kantor triple systems defined on tensor products of composition algebras.},
  author       = {Mondoc, Daniel},
  isbn         = {91-628-5513-1},
  issn         = {1404-0034},
  language     = {eng},
  number       = {9},
  publisher    = {Centre for the Mathematical sciences, Lund University},
  school       = {Lund University},
  series       = {Doctoral theses in mathematical sciences},
  title        = {Kantor Triple Systems},
  volume       = {2002},
  year         = {2002},
}