Abe, Toshikazu The equivalence of gyrocommutative gyrogroups and K-loops. (English) Zbl 1388.20073 Nihonkai Math. J. 28, No. 1, 69-78 (2017). Summary: It is known that gyrocommutative gyrogroups and K-loops are equivalent. This is a self-contained paper that presents the equivalence. Cited in 1 Document MSC: 20N05 Loops, quasigroups Keywords:gyrogroup; K-loop × Cite Format Result Cite Review PDF Full Text: Euclid References: [1] A. S. Basarab, K-loops, Izv. Akad. Nauk Respub. Moldova Mat. 1 (1992), 28-33, 90-91. [2] R. Beneduci and L. Molnár, On the standard K-loop structures of positive invertible elements in a \(C^*\)-algebra, J. Math. Anal. Appl. 420 (2014), 551-562. · Zbl 1308.46061 [3] H. Kiechle, Theory of K-loops, Lecture Notes in Mathematics, vol. 1778, Springer, Berlin, Heidelberg, 2002. · Zbl 0997.20059 [4] L. V. Sabinin, L. L. Sabinina and L. V. Sbitneva, On the notion of gyrogroup, Aequations Math. 56 (1998), 11-17. · Zbl 0923.20051 [5] R. U. Sexl and H. K. Urbantke, Relativity, groups, particles, Springer Physics. Springer-Verlag, Vienna, 2001. Special relativity and relativistic symmetry in field and particle physics, Revised and translated from the third German (1992) edition by Urbantke. · Zbl 0966.83502 [6] L. R. Soĭkis, The special loops, In Questions of the Theory of Quasigroups and Loops, Redakc.-Izdat. Otdel Akad. Nauk Moldav. SSR, Kishinev, 1970. [7] A. A. Ungar, Thomas rotation and the parametrization of the Lorentz transformation group, Found. Phys. Lett. 1 (1988), 57-89. [8] A. A. Ungar, The relativistic noncommutative nonassociative group of velocities and the Thomas rotation, Result. Math. 16 (1989), 168-179. · Zbl 0693.20067 [9] A. A. Ungar, Analytic Hyperbolic Geometry and Albert Einstein’s Special Theory of Relativity, World Scientific, 2008. · Zbl 1147.83004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.