Memoirs of the Faculty of Science, Shimane University

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Memoirs of the Faculty of Science, Shimane University 24
1990-12-25 発行

リー群上の等質左ループの射影性(II) : 局所理論

Projectivity of Homogeneous Left Loops on Lie Groups(II) : Local Theory
Kikkawa, Michihiko
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Description
Let G be a Lie group. An analytic local multiplication μ at the identity element 1 of G is associated with a Lie algebra on the tangent space of G at 1. It is shown that μ is a geodesic homogeneous local left loop which is in projective relation with the group multiplication μ^0 (Theorems 2.1 and 2.16), and that any geodesic homogeneous local left loop in projective relation with μ^0 is given by such a μ (Theorem 3.3).