2026-03-10T06:02:17Z https://fukuoka-edu.repo.nii.ac.jp/oai

oai:fukuoka-edu.repo.nii.ac.jp:00000965 2024-05-23T05:20:42Z 71:74:1715148028825

VALUATIONS OF LIE ALGEBRAS 坂本, 隆則 2702 サカモト, タカノリ SAKAMOTO, Takanori 本多, 政宣 2703 ホンダ, マサノブ HONDA, Masanobu ETYP:教育関連論文 We introduce the concept of valuations of Lie algebras and completions of valued Lie algebras. We show that if (L, | · |) is a valued Lie algebra then there is the unique completion (L , | · | ) up to isomorphism. We show that if a subalgebra H of L is a weak subideal of L (resp. a subideal of L, finitedimensional, soluble, nilpotent) then its topological closure H in (L , | · | ) is a weak subideal of L (resp. a subideal of L , finite-dimensional, soluble, nilpotent). We also introduce valuations |·| of the generalized Witt algebra WZ and present some properties of (W Z , | · |). Finally we illustrate the completion of (WZ, | · |) with a specific example. departmental bulletin paper 福岡教育大学 2019-03-10 application/pdf 福岡教育大学紀要. 第三分冊, 数学・理科・技術科編 68 1 13 Bulletin of University of Teacher Education Fukuoka. Part III, Mathematics, natural sciences and technology https://fukuoka-edu.repo.nii.ac.jp/record/965/files/3-01-坂本 隆則.pdf http://hdl.handle.net/10780/2119 https://fukuoka-edu.repo.nii.ac.jp/records/965 eng open access