Abstract
We show that any open ball centered at the origin of a complex inner product space endowed with a slightly modified Möbius addition is a gyrocommutative gyrogroup. A Möbius scalar multiplication by complex numbers can be naturally introduced so that some of the axioms of real inner product gyrovector spaces are satisfied. Moreover, the modified Möbius addition on the open ball of a complex inner product space can be characterized by three fundamental requirements.
Acknowledgments
The author is grateful to Dr. Abe for kindly sending me the reference [2]. The author would like to thank the referee for his/her valuable suggestion. This work was supported by the Research Institute for Mathematical Sciences, a Joint Usage/Research Center located in Kyoto University.
Citation
Keiichi Watanabe. "On a notion of complex Möbius gyrovector spaces." Nihonkai Math. J. 32 (2) 111 - 131, 2021.
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