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arXiv · 2102.11940

Geometric invariant decomposition of SU(3)

Martin Roelfs
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Abstract

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.

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Martin Roelfs. 2021-02-23. Geometric invariant decomposition of SU(3). https://doi.org/10.1007/s00006-022-01252-w

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