1998/02/25 by Helena Albuquerque, H. Albuquerque, Shahn Majid +3 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA
paper · pdf · doi:10.48550/arxiv.math/9802116
34 pages LATEX
arxiv created 1998/02/25 · arxiv updated 2009/11/30
We show that the octonions are a twisting of the group algebra of Z2 x Z2 x Z2 in the quasitensor category of representations of a quasi-Hopf algebra associated to a group 3-cocycle. We consider general quasi-associative algebras of this type and some general constructions for them, including quasi-linear algebra and representation theory, and an automorphism quasi-Hopf algebra. Other examples include the higher 2n-onion Cayley algebras and examples associated to Hadamard matrices.