Category Archives: SU(1,1)

Becoming anti de Sitter

Posted on 2017/05/14 by arkajad

In the last post we were discussing Killing vector fields of the group SL(2,R). It was done without specifying any reason for doing it – except that it somehow came in our way naturally. But now there is an opportunity … Continue reading →

Posted in Geometry, Hyperbolic geometry, SU(1,1) | 2 Comments

SL(2,R) Killing vector fields in coordinates

Posted on 2017/05/11 by arkajad

In Parametrization of SL(2,R) we introduced global coordinates on the group SL(2,R). Any matrix in SL(2,R) can be uniquely written as (1)   If is the matrix with components then its coordinates can be expressed as functions of the matrix … Continue reading →

Posted in Hyperbolic geometry, Mathematica, SU(1,1) | 3 Comments

Riemannian metrics – left, right and bi-invariant

Posted on 2017/05/09 by arkajad

The discussion in this post applies to Riemannian metrics on Lie groups in general, but we will concentrate on just one case in hand: SL(2,R). Let be a Lie group. Vectors tangent to paths in at identity form the Lie … Continue reading →

Posted in Geometry, Hyperbolic geometry, SU(1,1) | 2 Comments