Kostrikin, A. I.; Kostrikin, I. A.; Ufnarovskiĭ, V. A. On the uniqueness of orthogonal decompositions of Lie algebras of type \(A_n\) and \(C_n\). II. (Russian) Zbl 0536.17005 Mat. Issled. 74, 106-116 (1983). [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. Reviewer: Vyacheslav A. Artamonov (Moskva) Cited in 1 Document MSC: 17B20 Simple, semisimple, reductive (super)algebras Keywords:type \(C_2\); Killing form; orthogonal decomposition; simple Lie algebra; Cartan subalgebra Citations:Zbl 0536.17004 PDFBibTeX XMLCite \textit{A. I. Kostrikin} et al., Mat. Issled. 74, 106--116 (1983; Zbl 0536.17005) Full Text: EuDML