Coset Group Construction of Multidimensional Number Systems
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2014-07-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/6/3/578 |
| _version_ | 1811304349349969920 |
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| author | Horia I. Petrache |
| author_facet | Horia I. Petrache |
| author_sort | Horia I. Petrache |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T08:04:41Z |
| format | Article |
| id | doaj.art-527b3dbea35f4b6b8b1af868bfd0be98 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T08:04:41Z |
| publishDate | 2014-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-527b3dbea35f4b6b8b1af868bfd0be982022-12-22T02:55:11ZengMDPI AGSymmetry2073-89942014-07-016357858810.3390/sym6030578sym6030578Coset Group Construction of Multidimensional Number SystemsHoria I. Petrache0Department of Physics, Indiana University Purdue University Indianapolis, Indianapolis, IN 46202, USAExtensions 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.http://www.mdpi.com/2073-8994/6/3/578complex numbersquaternionsrepresentations |
| spellingShingle | Horia I. Petrache Coset Group Construction of Multidimensional Number Systems Symmetry complex numbers quaternions representations |
| title | Coset Group Construction of Multidimensional Number Systems |
| title_full | Coset Group Construction of Multidimensional Number Systems |
| title_fullStr | Coset Group Construction of Multidimensional Number Systems |
| title_full_unstemmed | Coset Group Construction of Multidimensional Number Systems |
| title_short | Coset Group Construction of Multidimensional Number Systems |
| title_sort | coset group construction of multidimensional number systems |
| topic | complex numbers quaternions representations |
| url | http://www.mdpi.com/2073-8994/6/3/578 |
| work_keys_str_mv | AT horiaipetrache cosetgroupconstructionofmultidimensionalnumbersystems |