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Octonions, simple Moufang loops and triality
Authors: Nagy G. P., Vojtechovský P.
– 0.39 Mb
Abstract
Nonassociative finite simple Moufang loops are exactly the loops constructed by Paige from Zorn vector matrix algebras. We prove this result anew, using geometric loop theory. In order to make the paper accessible to a broader audience, we carefully discuss the connections between composition algebras, simple Moufang loops, simple Moufang 3- nets, S-simple groups and groups with triality. Related results on multiplication groups, automorphisms groups and generators of Paige loops are provided.Gábor P. Nagy
Bolyai Institute,
University of Szeged,
Aradi vértanúk tere 1,
H-6720 Szeged,
Hungary.
E-mail:
________________________________
Petr Vojtechovský
Department of Mathematics,
University of Denver,
2360 S Gaylord St,
Denver, Colorado 80208,
U.S.A.
E-mail:
Bolyai Institute,
University of Szeged,
Aradi vértanúk tere 1,
H-6720 Szeged,
Hungary.
E-mail:
________________________________
Petr Vojtechovský
Department of Mathematics,
University of Denver,
2360 S Gaylord St,
Denver, Colorado 80208,
U.S.A.
E-mail:
Fulltext
– 0.39 Mb
Contents
- Check character systems over quasigroups and loops
- Quasigroups constructed from cycle systems
- Octonions, simple Moufang loops and triality
- See Otter digging for algebraic pearls
- Quasigroup permutation representations
