论文标题
集市代数的截面非缔合率
Sectional nonassociativity of metrized algebras
论文作者
论文摘要
代数（不一定是关联或Unital）代数的截面非缔合率与伪 - 利曼式公制的截面曲率相似，并与联合者代替了Levi-Civita Covariant衍生产品。对于通勤性的实际代数，非负分段非缔合性通常称为诺顿不平等，而在赫尔特尼亚矩阵的约旦代数的截面非缔合性上的尖锐上限与真正的hurwitz代数相对于Böttcher-Wenzel-Wenzel-Chern-Chern-Chern-Chern-do Carmo-kobaysequality。解释了这些和其他基本示例，并描述了一些界限对交换代数的分段非缔合性的一些后果。技术的一个兴趣点是，结果在八元中以及协会的赫尔维兹代数方面起作用。
The sectional nonassociativity of a metrized (not necessarily associative or unital) algebra is defined analogously to the sectional curvature of a pseudo-Riemannian metric, with the associator in place of the Levi-Civita covariant derivative. For commutative real algebras nonnegative sectional nonassociativity is usually called the Norton inequality, while a sharp upper bound on the sectional nonassociativity of the Jordan algebra of Hermitian matrices over a real Hurwitz algebra is closely related to the Böttcher-Wenzel-Chern-do Carmo-Kobayashi inequality. These and other basic examples are explained, and there are described some consequences of bounds on sectional nonassociativity for commutative algebras. A technical point of interest is that the results work over the octonions as well as the associative Hurwitz algebras.
