number of downloads : ?
Title Transcription
トウシツ ループ ノ ヒダリ イドウ ニツイテ
Title Alternative (English)
On the Left Translations of Homogeneous Loops
File
language
eng
Author
Kikkawa, Michihiko
Description
The notion of homogeneous systems inntroduced in §1 of this paper is an abstraction of homogeneity
of homogeneous loops and groups. In consideration of the geometric approach tried in [1], the left translatious of homogeneous Lie loops lead us to the notion of (parallel) displacements of homogeneous systems. This paper is aimed at the axiomatic construction of homogeneous systems which will be useful to the study of a certain class of locally reductive spaces including homogemeous Lie loops and Lie groups. In §2 the homogeneous systems of homogeneous loops are found. In §3 it is shown that any autornorphism of a homogeneous systems is an automorphism fixing the origin followed by a displacement from the origin. As the isotropy subgroup of the group of displacements the notion of holonomy groups is obtained which is closely related with (non) associativity of the binary system induced from the homogeneous system. Symmetric homogueous systems are introduced in §4 which should be combined with symmetric homogeneous spaces.
Journal Title
Memoirs of the Faculty of Literature and Science, Shimane University. Natural sciences
Volume
10
Start Page
19
End Page
25
ISSN
03709434
Published Date
1976-12-20
NCID
AN0010806X
Publisher
島根大学文理学部
Publisher Aalternative
The Faculty of Literature and Science, Shimane University
NII Type
Departmental Bulletin Paper
OAI-PMH Set
Faculty of Science and Engineering
他の一覧
このエントリーをはてなブックマークに追加