论文标题
具有非排定痕量形式和无痕量倍增的内态性的换向代数
Commutative algebras with nondegenerate invariant trace form and trace-free multiplication endomorphisms
论文作者
论文摘要
如果其乘法内态性不含痕迹，并且如果其杀死类型的痕量形式不变且不变，则确切的代数是确切的。杀死的Metrized确切的交换代数一定不是Unitital也不是联合性的。这样的代数可以看作是半神经代数的交换类似物，也可以视为étale（联想）代数的非缔合概括。描述了一些基本示例，并引入了非缔合性的定量度量，与连接的曲率正式相似，这些量子促进了这些代数的组织和表征。
A commutative algebra is exact if its multiplication endomorphisms are trace-free and is Killing metrized if its Killing type trace-form is nondegenerate and invariant. A Killing metrized exact commutative algebra is necessarily neither unital nor associative. Such algebras can be viewed as commutative analogues of semisimple Lie algebras or, alternatively, as nonassociative generalizations of étale (associative) algebras. Some basic examples are described and there are introduced quantitative measures of nonassociativity, formally analogous to curvatures of connections, that serve to facilitate the organization and characterization of these algebras.
