Graded algebras; Non commutative and non associative algebras; octonions
Abstract :
[en] We study the series of complex nonassociative algebras $\bbO_n$ and real nonassociative algebras $\bbO_{p,q}$ introduced in~\cite{MGO2011}.
These algebras generalize the classical algebras of octonions and Clifford algebras. The algebras $\bbO_{n}$ and $\bbO_{p,q}$ with $p+q=n$ have a natural $\Z_2^n$-grading, and they are
characterized by cubic forms over the field $\Z_2$. We establish a periodicity for the algebras~$\bbO_{n}$ and $\bbO_{p,q}$ similar to that of the Clifford algebras $\mathrm{Cl}_{n}$ and~$\mathrm{Cl}_{p,q}$.
Disciplines :
Mathematics
Author, co-author :
Kreusch, Marie ; Université de Liège - ULiège > Département de mathématique > Géométrie et théorie des algorithmes
Language :
English
Title :
Bott type periodicity for the higher octonions
Publication date :
2016
Journal title :
Journal of Noncommutative Geometry
ISSN :
1661-6952
eISSN :
1661-6960
Publisher :
European Mathematical Society Publishing House, Zurich, Switzerland
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