JournalsjncgVol. 9, No. 4pp. 1201–1225

Bott type periodicity for the higher octonions

  • Marie Kreusch

    Université de Liège, Belgium
Bott type periodicity for the higher octonions cover

Abstract

We study the series of complex nonassociative algebras On\mathbb O_{n} and real nonassociative algebras Op,q\mathbb O_{p,q} introduced in [10]. These algebras generalize the classical algebras of octonions and Clifford algebras. The algebras On\mathbb O_{n} and Op,q\mathbb O_{p,q} with p+q=np+q=n have a natural Z2n\mathbb Z_2^n-grading, and they are characterized by cubic forms over the field Z2\mathbb Z_2. We establish a periodicity for the algebras On\mathbb O_{n} and Op,q\mathbb O_{p,q} similar to that of the Clifford algebras Cln\mathrm {Cl}_{n} and Clp,q\mathrm {Cl}_{p,q}.

Cite this article

Marie Kreusch, Bott type periodicity for the higher octonions. J. Noncommut. Geom. 9 (2016), no. 4, pp. 1201–1225

DOI 10.4171/JNCG/221