Central elements in the universal enveloping algebras for the split realization of the orthogonal Lie algebras
The split realization of \(\mathfrak{o}(M)\) is defined as \(\mathfrak{o}(M)=\{X\in\mathrm{Mat}_n(\mathbb{C}):{}^tXM+MX=0\}\), where \(M\) is the symmetric \(n\times n\)-matrix \((\delta_{i,n+1-j})_{1\leq i,j\leq n}\). For the universal enveloping algebra of \(U(\mathfrak{o}(M))\) the author gives explicit formulae for certain central elements. The main ingredients of the formulae are certain column determinants. It is further proved that these central elements form a generating set of the center of \(U(\mathfrak{o}(M))\).
scientific article; zbMATH DE number 5159803
scientific article