zbMATH — the first resource for mathematics

On the uniqueness of orthogonal decompositions of Lie algebras of type \(A_n\) and \(C_n\). II. (Russian) Zbl 0536.17005
[For part I see the preceding review Zbl 0536.17004.] Let \(L\) be a finite dimensional complex simple Lie algebra. An orthogonal decomposition \(L=\oplus H_j\) is an orthogonal sum (relative to the Killing form) of Cartan subalgebras \(H_j\). The main result of the paper states that an orthogonal decomposition of a simple Lie algebra of type \(C_2\) is unique up to conjugation. The authors indicate an explicit form of orthogonal decompositions of \(L=C_2\) containing the Cartan subalgebra \(H_0\subset L\) of all diagonal matrices.

17B20 Simple, semisimple, reductive (super)algebras
Full Text: EuDML