On eight-dimensional unital division algebras over finite fields

ABSTRACT

The purpose of this paper is to investigate the eight-dimensional non-associative unital division algebras {0}≠A over finite fields, admitting elementary abelian 2-group of automorphisms E≤Aut(A), of order 8, using tools from algebraic geometry.

KEYWORDS:

• Homogeneous polynomial
• Lang–Weil theorem
• Nim-addition
• structure-constant

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 14A75
• 17A45

Acknowledgment

The author would like to thank the Public Authority for Applied Education and Training, for supporting and funding this research project No. BE-15-01 and the referee for his valuable remarks.