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

TL;DR

This paper constructs explicit generators for the center of the universal enveloping algebra of complex orthogonal Lie algebras, utilizing the Iwasawa decomposition and alternative matrix representations.

Contribution

It introduces a novel method for constructing generators of the center using the Iwasawa decomposition and alternative matrices for orthogonal Lie algebras.

Findings

Explicit generators for the center are constructed.

The approach aligns with the Iwasawa decomposition.

Discussion of the Pfaffian's Iwasawa decomposition.

Abstract

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.