H. I. Petrache: Coset Group Construction of Multidimensional Number Systems

Horia I. Petrache, Symmetry 2014, Vol. 6(3), pp. 578-588; doi:10.3390/sym6030578

Online: http://www.mdpi.com/2073-8994/6/3/578, http://arxiv.org/abs/1212.1850

Abstract: 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.

Source: http://www.mdpi.com/2073-8994/6/3/578, http://arxiv.org/abs/1212.1850


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