Eigentheory of Cayley-Dickson algebras
We show how eigentheory clarifies many algebraic properties of Cayley-Dickson algebras. These notes are intended as background material for those who are studying this eigentheory more closely.
math.RA↗
arXiv subjects
Daniel K. Biss
Publications and source records attributed to Daniel K. Biss.
Large annihilators in Cayley-Dickson algebras II
We establish many previously unknown properties of zero-divisors in Cayley-Dickson algebras. The basic approach is to use a certain splitting that simplifies computations surprisingly.
math.RA↗
Large annihilators in Cayley-Dickson algebras
Cayley-Dickson algebras are an infinite sequence of non-associative algebras starting with the reals, complexes, quaternions, and octonions. We study the zero-divisors in the higher Cayley-Dickson algebras. In particular, we show that the annihilator of any element in the 2^n-dimensional Cayley-Dickson algebra has dimension at most 2^n-4n+4. Moroever, every multiple of four between 0 and this upper bound actually occurs as the dimension of some annihilator (a theorem of Moreno says that only multiples of four can occur). We completely describe all the zero-divisors whose annihilator has dimension 2^n-4n+4.
math.RA↗