Boosts in Lorentz-Minkowski space $\mathbb{L}^3$ (or $E_{1}^3$) (+ material) Can someone give me examples of boosts in $\mathbb{L}^3$? I understand that boosts are isometries that leave pointwise fixed a straight line $\mathcal{L}$. The only thing I can think of, until now, are rotations around said $\mathcal{L}$.
I'm using $\operatorname{diag}[1,1,-1]$, that is, $\langle (x_1,y_1,z_1), (x_2,y_2,z_2)\rangle = x_1x_2 + y_1y_2 - z_1z_2$.
I'm using this text to study. Also, I'm having trouble finding more material on this. Everywhere I find anything about the subject, it is more related to physics than differential geometry, which makes it harder for me to understand. Can someone share something, please? Thanks in advance!

http://www.dm.uniba.it/geloba2009/PresentazioniGeLoBa2009/Ortega.pdf
Try that...and try to find S. Haesen stuff
