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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.04683 |
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| _version_ | 1866913659639300096 |
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| author | Courchesne, Derek Tremblay, Sébastien |
| author_facet | Courchesne, Derek Tremblay, Sébastien |
| contents | In this article we study some algebraic aspects of multicomplex numbers $\mathbb M_n$. For $n\geq 2$ a canonical representation is defined in terms of the multiplication of $n-1$ idempotent elements. This representation facilitates computations in this algebra and makes it possible to introduce a generalized conjugacy $Λ_n$, i.e. a composition of the $n$ multicomplex conjugates $Λ_n:=\dagger_1\cdots \dagger_n$, as well as a multicomplex norm. The ideals of the ring of multicomplex numbers are then studied in details, free $\mathbb M_n$-modules and their linear operators are considered and, finally, we develop Hilbert spaces on the multicomplex algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04683 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multicomplex Ideals, Modules and Hilbert Spaces Courchesne, Derek Tremblay, Sébastien Mathematical Physics Rings and Algebras In this article we study some algebraic aspects of multicomplex numbers $\mathbb M_n$. For $n\geq 2$ a canonical representation is defined in terms of the multiplication of $n-1$ idempotent elements. This representation facilitates computations in this algebra and makes it possible to introduce a generalized conjugacy $Λ_n$, i.e. a composition of the $n$ multicomplex conjugates $Λ_n:=\dagger_1\cdots \dagger_n$, as well as a multicomplex norm. The ideals of the ring of multicomplex numbers are then studied in details, free $\mathbb M_n$-modules and their linear operators are considered and, finally, we develop Hilbert spaces on the multicomplex algebra. |
| title | Multicomplex Ideals, Modules and Hilbert Spaces |
| topic | Mathematical Physics Rings and Algebras |
| url | https://arxiv.org/abs/2405.04683 |