Bott type periodicity for the higher octonions

2014/05/26 by Kreusch, Marie
#Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1405.6521

Abstract

We study the series of complex nonassociative algebras On and real nonassociative algebras O_p,q introduced in [10]. These algebras generalize the classical algebras of octonions and Clifford algebras. The algebras O_n and O_p,q with p + q = n have a natural Z_n²-grading, and they are characterized by cubic forms over the field Z₂. We establish a periodicity for the algebras O_n and O_p,q similar to that of the Clifford algebras Cln and Cl_p,q.

Related

• Beyond Octonions
• Classification of the algebras \mathbbO_p,q
• Complex Bott Periodicity in algebraic geometry
• Clifford algebras obtained by twisting of group algebras
• A Bott periodicity proof for real graded C^∗-algebras