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Kikkawa loops and homogeneous loops

Michihiko Kikkawa (2004)

Commentationes Mathematicae Universitatis Carolinae

In H. Kiechle's publication ``Theory of K-loops'' [3], the name Kikkawa loops is given to symmetric loops introduced by the author in 1973. This concept started from an analogical imagination of sum of vectors in Euclidean space brought up on a sphere. In 1975, this concept was extended by him to the more general concept of homogeneous loops, and it led us to a non-associative generalization of the theory of Lie groups. In this article, the backstage of finding these concepts will be disclosed from...

Knots in S 2 x S 1 derived from Sym(2, ℝ)

Sang Lee, Yongdo Lim, Chan-Young Park (2000)

Fundamenta Mathematicae

We realize closed geodesics on the real conformal compactification of the space V = Sym(2, ℝ) of all 2 × 2 real symmetric matrices as knots or 2-component links in S 2 × S 1 and show that these knots or links have certain types of symmetry of period 2.

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