Clifford纤维和可能的动力学
Clifford Fibrations and Possible Kinematics
摘要：
继Herranz和Santander之后[Herranz F. J.，Santander M.，Mem. Real Acad. Cienc。确切菲斯自然。Madrid 32（1998），59-84，physics/9702030]我们将基于可能的运动学代数和群构造齐性空间[Bacry H.，莱维-勒布隆德M.，J. Math.Phys.9（1967），1605-1614]及其对二维时空的压缩。我们的构造是不同的，因为它是基于广义Clifford纤维化：Alfred A.克诺夫公司，纽约，2005]我们将称我们的纤维化为Clifford纤维化而不是Hopf纤维化，因为我们的纤维化是一个几何构造。纤维化的简单代数性质描述了运动学代数和群的几何性质，以及由它们导出的时空。我们开发了一个代数框架，处理所有可能的运动代数保存一个，静态代数。
英文摘要：
Following Herranz and Santander [Herranz F.J., Santander M., Mem. Real Acad. Cienc. Exact. Fis. Natur. Madrid 32 (1998), 59-84, physics/9702030] we will construct homogeneous spaces based on possible kinematical algebras and groups [Bacry H., Levy-Leblond J.-M., J. Math. Phys. 9 (1967), 1605-1614] and their contractions for 2-dimensional spacetimes. Our construction is different in that it is based on a generalized Clifford fibration: Following Penrose [Penrose R., Alfred A. Knopf, Inc., New York, 2005] we will call our fibration a Clifford fibration and not a Hopf fibration, as our fibration is a geometrical construction. The simple algebraic properties of the fibration describe the geometrical properties of the kinematical algebras and groups as well as the spacetimes that are derived from them. We develop an algebraic framework that handles all possible kinematic algebras save one, the static algebra.
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