A construction of generators of $Z(\mathfrak{so}_{n})$

We construct generators of the center of the universal enveloping algebra of the complex orthogonal Lie algebra realized as the alternative matrices of size $n$. These elements are constructed in accordance with the Iwasawa decomposition of the real rank one indefinite orthogonal Lie algebra. We also discuss the Iwasawa decomposition of the Pfaffian.

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