Coset Group Construction of Multidimensional Number Systems

Symmetry

关键词: complex numbers;    quaternions;    representations;   

DOI  :  10.3390/sym6030578

来源: mdpi

【 摘 要 】

Extensions of real numbers in more than two dimensions, in particular quaternions and octonions, are finding applications in physics due to the fact that they naturally capture symmetries of physical systems. However, in the conventional mathematical construction of complex and multicomplex numbers multiplication rules are postulated instead of being derived from a general principle. A more transparent and systematic approach is proposed here based on the concept of coset product from group theory. It is shown that extensions of real numbers in two or more dimensions follow naturally from the closure property of finite coset groups adding insight into the utility of multidimensional number systems in describing symmetries in nature.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland