DOI QR코드

DOI QR Code

Distributivity on the Gyrovector Spaces

Kim, Sejong

  • Received : 2014.03.03
  • Accepted : 2014.07.14
  • Published : 2015.03.23

Abstract

As a vector space provides a fundamental tool for the study of Euclidean geometry, a gyrovector space provides an algebraic tool for the study of hyperbolic geometry. In general, the gyrovector spaces do not satisfy the distributivity with scalar multiplication. In this article, we see under what condition the distributivity with scalar multiplication is satisfied.

Keywords

gyrogroup;gyrovector space;gyroautomorphism

References

  1. L. V. Sabinin, L. L. Sabinin, and L. V. Sbitneva, On the notion of a gyrogroup, Aequ. Math., 56(1998), 11-17. https://doi.org/10.1007/s000100050039
  2. A. A. Ungar, Analytic hyperbolic geometry and Albert Einstein's special theory of relativity, World Scientific Press, 2008.