Extension of the Unit Disk Gyrogroup into the Unit Ball of Any Real Inner Product Space
Copyright policy )Extension of the Unit Disk Gyrogroup into the Unit Ball of Any Real Inner Product Space
The author generalizes his example of a gyrogroup (= \(k\)-loop = Bruck loop), which he has defined previously [Aequationes Math. 47, No. 2-3, 240-254 (1994; Zbl 0799.20032)] in the open disc \(D_c:=\{x\in\mathbb{C}\mid|x|0\) by \(x\oplus y:=(x+y)c^2\cdot(c^2+\overline xy)^{-1}\), for the case that \(D_c\) is replaced by an open ball \(V_c:=\{{\mathfrak x}\in V\mid|{\mathfrak x}|
- North Dakota State University United States
Special relativity, Loops, quasigroups, Extensions, wreath products, and other compositions of groups, Bruck loops, Applied Mathematics, real inner product spaces, generalized Poincaré metric, Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.), open balls, Monogenic and polygenic functions of one complex variable, \(k\)-loops, hyperbolic spaces, gyrogroups, Möbius transformations, Structure and representation of the Lorentz group, motion groups, Analysis
Special relativity, Loops, quasigroups, Extensions, wreath products, and other compositions of groups, Bruck loops, Applied Mathematics, real inner product spaces, generalized Poincaré metric, Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.), open balls, Monogenic and polygenic functions of one complex variable, \(k\)-loops, hyperbolic spaces, gyrogroups, Möbius transformations, Structure and representation of the Lorentz group, motion groups, Analysis
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