Binary Representation in Multicomplex and Clifford Algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915519301419008 |
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| author | Courchesne, Derek Tremblay, Sébastien |
| author_facet | Courchesne, Derek Tremblay, Sébastien |
| contents | Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise operation. This result covers both multicomplex and Clifford algebras of any dimension. Necessary conditions for the existence of a diagonal basis are derived directly from this result, with an algorithm-like method to obtain it through a change-of-coordinates matrix in the commutative case. The same framework is then used to define an algebra of conjugate operations and study its properties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_23369 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Binary Representation in Multicomplex and Clifford Algebras Courchesne, Derek Tremblay, Sébastien Mathematical Physics Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise operation. This result covers both multicomplex and Clifford algebras of any dimension. Necessary conditions for the existence of a diagonal basis are derived directly from this result, with an algorithm-like method to obtain it through a change-of-coordinates matrix in the commutative case. The same framework is then used to define an algebra of conjugate operations and study its properties. |
| title | Binary Representation in Multicomplex and Clifford Algebras |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2509.23369 |