Large annihilators in Cayley-Dickson algebras
环与代数
2007-05-23 v1 代数拓扑
摘要
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.
引用
@article{arxiv.math/0511691,
title = {Large annihilators in Cayley-Dickson algebras},
author = {Daniel K. Biss and Daniel Dugger and Daniel C. Isaksen},
journal= {arXiv preprint arXiv:math/0511691},
year = {2007}
}