Group-Like Structure Underlying the Unit Ball in Real Inner Product Spaces
Group-Like Structure Underlying the Unit Ball in Real Inner Product Spaces
复制标题
实内积空间中单位球的类群结构
DOI：
10.1007/bf03323180
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发表时间：
1990
影响因子：
2.2
通讯作者：
A. Ungar
中科院分区：
文献类型：
--
作者：
A. Ungar
相对论速度相加定律和狭义相对论的Thomas旋转的抽象产生了一种方法，使单位球在任何实内积空间中具有类群结构，其中标准的结合-交换定律通过Thomas旋转而松弛。由此得到的类群对象称为完全弱结合交换群胚。任何完全的WACG都可以推广到一个类似于狭义相对论的洛伦兹群的群。
Abstraction of the relativistic velocity addition law and of the Thomas rotation of the special theory of relativity yields a means of endowing the unit ball in any real inner product space with a group- like structure, in which the standard associative- commutative laws are relaxed by means of the Thomas rotation. The resulting group- like object is called a complete weakly associative- commutative groupoid. Any complete WACG can be extended to a group analogous to the Lorentz group of the special theory of relativity.