We study the series of complex nonassociative algebras and real nonassociative algebras introduced in . These algebras generalize the classical algebras of octonions and Clifford algebras. The algebras and with have a natural -grading, and they are characterized by cubic forms over the field . We establish a periodicity for the algebras and similar to that of the Clifford algebras and .
Cite this article
Marie Kreusch, Bott type periodicity for the higher octonions. J. Noncommut. Geom. 9 (2016), no. 4, pp. 1201–1225