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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2102.11940 |
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| _version_ | 1866917013726691328 |
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| author | Roelfs, Martin |
| author_facet | Roelfs, Martin |
| contents | A novel invariant decomposition of diagonalizable $n \times n$ matrices into $n$ commuting matrices is presented. This decomposition is subsequently used to split the fundamental representation of $\mathfrak{su}(3)$ Lie algebra elements into at most three commuting elements of $\mathfrak{u}(3)$. As a result, the exponential of an $\mathfrak{su}(3)$ Lie algebra element can be split into three commuting generalized Euler's formulas, or conversely, a Lie group element can be factorized into at most three generalized Euler's formulas. After the factorization has been performed, the logarithm follows immediately. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_11940 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Geometric invariant decomposition of SU(3) Roelfs, Martin Mathematical Physics A novel invariant decomposition of diagonalizable $n \times n$ matrices into $n$ commuting matrices is presented. This decomposition is subsequently used to split the fundamental representation of $\mathfrak{su}(3)$ Lie algebra elements into at most three commuting elements of $\mathfrak{u}(3)$. As a result, the exponential of an $\mathfrak{su}(3)$ Lie algebra element can be split into three commuting generalized Euler's formulas, or conversely, a Lie group element can be factorized into at most three generalized Euler's formulas. After the factorization has been performed, the logarithm follows immediately. |
| title | Geometric invariant decomposition of SU(3) |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2102.11940 |