Quasialgebra structure of the octonions
Abstract
We show that the octonions are a twisting of the group algebra of Z_2 x Z_2 x Z_2 in the quasitensor category of representations of a quasiHopf algebra associated to a group 3cocycle. We consider general quasiassociative algebras of this type and some general constructions for them, including quasilinear algebra and representation theory, and an automorphism quasiHopf algebra. Other examples include the higher 2^nonion Cayley algebras and examples associated to Hadamard matrices.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 1998
 DOI:
 10.48550/arXiv.math/9802116
 arXiv:
 arXiv:math/9802116
 Bibcode:
 1998math......2116A
 Keywords:

 Quantum Algebra
 EPrint:
 34 pages LATEX