A Geometric Environment for Building up Loops

作者:Pasotti Stefano*; Pianta Silvia; Zizioli Elena
来源:Results in Mathematics, 2015, 68(3-4): 415-426.
DOI:10.1007/s00025-015-0449-z

摘要

We start from the embedding of the Klein model of a hyperbolic plane over a Euclidean field in its direct motion group and of both in . We present a geometric procedure to obtain loops which are related to suitable regular subsets of direct motions as transversals of the coset space , where is the subgroup of hyperbolic rotations fixing a given point . We investigate some properties of such loops and we determine their automorphism groups.

  • 出版日期2015-11