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島根大学理学部紀要 16 巻
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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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）.
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