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リー サンコウ ダイスウ ノ カカイセイ ニ カンスル チュウイ
日本語以外のタイトル
Remaraks on Solvability of Lie Triple Algebras
ファイル
言語
英語
著者
吉川 通彦
内容記述(抄録等)
The class of Lie triple algebras contains Lie algebras and Lie triple systems as special classes. Therefore, the study of Lie triple algebras may need to generalize various concepts in the theory of Lie algebras and Lie triple systems to those in Lie triple algebras. In this paper, we try to introduce the concept of solvability of Lie triple algebras (§1), although their detailed properties are not yet found satisfactorily. We show that both of the standard enveloping Lie algebra and inner derivation algebra of a Lie triplle algebra g are solvable if g is solvable. In §2, the existence of the radical of Lie triple algebras is shown and some results about semi-simple Lie triple algebras are given, under the solvability introduced in S I . The general theory of Lie triple algebras seems to play an important role in the theory of analytic homogeneous systems since it is proved in [1] that every connected and simply connected analytic homogeneous system is characterized by its tangent Lie triple algebra.
掲載誌名
島根大学理学部紀要
13
開始ページ
17
終了ページ
22
ISSN
03879925
発行日
1979-12-20
NCID
AN00108106
出版者
島根大学理学部
出版者別表記
The Faculty of Science, Shimane University
資料タイプ
紀要論文
部局
総合理工学部
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