Vol. 96, No. 1, 1981

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On Killing-Ricci forms of Lie triple algebras

Michihiko Kikkawa

Vol. 96 (1981), No. 1, 153–161

The notion of Killing-Ricci forms of Lie triple algebras is introduced as a generalization of both of Killing forms of Lie algebras and the Ricci forms of the tangent Lie triple systems of Riemannian symmetric spaces. For a class of Lie triple algebras G, it is shown that G is decomposed into a direct sum of simple ideals if its Killing-Ricci form is nondegenerate. As an application, structure of the reductive pair consisting of a semi-simple Lie algebra and its semi-simple subalgebra is investigated.

Mathematical Subject Classification 2000
Primary: 17B20
Secondary: 53C35
Received: 30 May 1980
Published: 1 September 1981
Michihiko Kikkawa