Advances in Mathematical Physics
Volume 2010 (2010), Article ID 956128, 9 pages
Research Article

Arnold's Projective Plane and r-Matrices

Tokyo University of Science, Wakamiya, 26 Shinjyuku, Tokyo, Japan

Received 19 December 2009; Accepted 27 February 2010

Academic Editor: A. Yoshioka

Copyright © 2010 K. Uchino. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We will explain Arnold's 2-dimensional (shortly, 2D) projective geometry (Arnold, 2005) by means of lattice theory. It will be shown that the projection of the set of nontrivial triangular r-matrices is the pencil of tangent lines of a quadratic curve on Arnold's projective plane.