島根大学理学部紀要

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島根大学理学部紀要 16
1982-12-25 発行

リー三項代数の不変形式に関する注意

Remarks on Invariant Forms of Lie Triple Algebras
吉川 通彦
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内容記述(抄録等)
Invariant forms of Lie triple algebras have been introduced in[3]as generalizations of those of Lie algebras and Lie tripie systems. In this paper,the meaning of the definition((2.1)and (2.2))of invariant forms is clarified from a viewpoint of invariance under endomorphisms of the Lie triple algebra(Proposition 3).The main theorem shows that there exists a one-to-one correspondence between the set of all invariant forms of a Lie tripie aigebra g and the set of invariant forms ofits standard enveioping Lie algebra A = g【○!+】D(g,g)satisfyiing the orthogonal condition g⊥D(g,g).