度量代数的截面非结合性
环与代数
2024-01-19 v3
摘要
度量（不一定结合或含单位元）代数的截面非结合性定义方式类似于伪黎曼度量的截面曲率，以结合子代替 Levi-Civita 协变导数。对于交换实代数，非负截面非结合性通常称为 Norton 不等式，而实 Hurwitz 代数上 Hermitian 矩阵 Jordan 代数的截面非结合性的锐上界与 Böttcher-Wenzel-Chern-do Carmo-Kobayashi 不等式密切相关。我们解释了这些及其他基本例子，并描述了截面非结合性界对交换代数的一些推论。一个引人关注的技术点是，这些结果在八元数以及结合 Hurwitz 代数上同样成立。
引用
@article{arxiv.2211.01073,
title = {Sectional nonassociativity of metrized algebras},
author = {Daniel J. F. Fox},
journal= {arXiv preprint arXiv:2211.01073},
year = {2024}
}
备注
v3: Added missing "nontrivial" in the statement of Lemma 8.6 and eliminated from its proof an incorrect argument using an unnecessary hypothesis that has also been removed from its statement. The change has no further ramifications in the paper