Geometric invariant decomposition of SU(3)

DOI10.1007/S00006-022-01252-WarXiv2102.11940MaRDI QIDQ6361395

Martin Roelfs

Publication date: 23 February 2021

Abstract: A novel invariant decomposition of diagonalizable $nimesn$ matrices into $n$ commuting matrices is presented. This decomposition is subsequently used to split the fundamental representation of $mathfraksu(3)$ Lie algebra elements into at most three commuting elements of $mathfraku(3)$. As a result, the exponential of an $mathfraksu(3)$ 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.

Mathematics Subject Classification ID

Commutativity of matrices (15A27) Clifford algebras, spinors (15A66) Matrix Lie algebras (15B30)

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