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島根大学理学部紀要 22 巻
1988-12-25 発行
R^n上の左ループの射影性
Projectivity of Left Loops on R^n
吉川 通彦
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Left loops and their projective transformations are considered on analytic manifolds. It is shown that there exists a one-to-one correspondence between the isomorphism classes of the images of the abelian Lie group R_n under projective transformations of left loops and the isomorphism classes of real Lie algebras of dimension n (Theorem 1). For any left loop in projective relation with R_n, the correspondence between normal left subloops and ideals of the tangent Lie triple algebra is established (Theorem 2).
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