论文标题
仿射空间和时空的手性
Chirality in Affine Spaces and in Spacetime
论文作者
论文摘要
当对象的对称组不包含间接等距时，对象是手性。除了在欧几里得病例中，很难将异构体分类为直接或间接。我们在等轴测组的外部半程产物的帮助下对它们进行了分类，尤其是在有限维真实二次空间上定义的仿射空间的情况下。我们还归类为直接或间接的真实洛伦兹 - 米科夫斯基时空以及由牛顿 - 卡丹理论定义的经典时空的异构体。
An object is chiral when its symmetry group contains no indirect isometry. It can be difficult to classify isometries as direct or indirect, except in the Euclidean case. We classify them with the help of outer semidirect products of isometry groups, in particular in the case of an affine space defined over a finite-dimensional real quadratic space. We also classify as direct or indirect the isometries of the real Lorentz-Minkowski spacetime and those of the classical spacetime defined by the Newton-Cartan theory.
