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Title Transcription
タイショウ クウカン ノ ダイスウテキ モデル トシテノ ジュングン ニツイテ
Title Alternative (English)
On Some Quasigroups of Algebraic Models of Symmetric Spaces
File
language
eng
Author
Kikkawa, Michihiko
Description
In the previous paper [4], we have studied a characterization of linearly connected manifolds with parallel torsion and curvature by their tangent algebras. Lie algebra Lie group correspondence and Lie triple system symmetric space correspondence are found there in the special cases.
On the other hand, as a generalization of Lie group with ( - ) -connection of Cartan, we have a binary-systematic characterization of linearly connected manifold in our minds. From such a view point, we shall try to present in this note a quasigroup, called a symmetric loop, as an algebraic model of symmetric space. In [5], O. Loos has introduced an axiomatic binary system in symmetric space and defined the symmetric space by means of the multiplication. We were motivated by this work to construct the symmetric loop.
At the last part of the present note, the family of all left translations of the symmetric loop will be observed on the lines of Lie triple family of transformations of T.Nono [6].
Journal Title
Memoirs of the Faculty of Literature and Science, Shimane University. Natural sciences
Volume
6
Start Page
9
End Page
13
ISSN
03709434
Published Date
1973-03-10
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
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