caa a22 4500 475807669 CHVBK 20180406123751.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1023/A:1008399914122 doi (NATIONALLICENCE)springer-10.1023/A:1008399914122 Constructions for Octonion and Exceptional Jordan Algebras [Elektronische Daten] [L. Rylands, D. Taylor] In this note we reverse theusual process of constructing the Lie algebras of types G 2and F 4 as algebras of derivations of the splitoctonions or the exceptional Jordan algebra and instead beginwith their Dynkin diagrams and then construct the algebras togetherwith an action of the Lie algebras and associated Chevalley groups.This is shown to be a variation on a general construction ofall standard modules for simple Lie algebras and it is well suitedfor use in computational algebra systems. All the structure constantswhich occur are integral and hence the construction specialisesto all fields, without restriction on the characteristic, avoidingthe usual problems with characteristics 2 and 3. Kluwer Academic Publishers, 2000 Exceptional Jordan algebras nationallicence octonions nationallicence Lie algebras of type G 2, F 4 nationallicence Rylands L. School of Science, University of Western Sydney, Nepean, Australia aut Taylor D. School of Mathematics and Statistics, University of Sydney, 2006, NSW, Australia aut Designs, Codes and Cryptography Kluwer Academic Publishers 21/1-3(2000-10-01), 191-203 0925-1022 21:1-3<191 2000 21 10623 https://doi.org/10.1023/A:1008399914122 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008399914122 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rylands L. School of Science, University of Western Sydney, Nepean, Australia aut NATIONALLICENCE 700 1- Taylor D. School of Mathematics and Statistics, University of Sydney, 2006, NSW, Australia aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 21/1-3(2000-10-01), 191-203 0925-1022 21:1-3<191 2000 21 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer