File:PSL-PGL.svg

Original file (SVG file, nominally 491 × 254 pixels, file size: 70 KB)

Summary

Description
English: Commutative diagram showing the projective linear groups (special and general) and their relations
Date
Source Own work, created as per: en:meta:Help:Displaying a formula#Commutative diagrams; source code below.
Author Nils R. Barth

LaTeX source

\documentclass{amsart} \usepackage[all, ps, dvips]{xy} % Loading the XY-Pic package                                 % Using postscript driver for smoother                                 % curves \usepackage{color}              % For invisible frame \begin{document} \thispagestyle{empty} % No page numbers \SelectTips{eu}{}     % Euler arrowheads (tips) \setlength{\fboxsep}{0pt} % Frame box margin {\color{white}\framebox{{\color{black}$$ % Frame for margin  \xymatrix{    \mathrm{SZ}(V)         \ar@{^(->}[r]                      \ar@{^(->}[d]  & \mathrm{Z}(V)\cong F^* \ar@{->>}[r]^(.6){\det \cong z^n}  \ar@{^(->}[d]  & (F^*)^n                                                   \ar@{^(->}[d] \\    \mathrm{SL}(V)         \ar@{^(->}[r]                  \ar@{->>}[d]  & \mathrm{GL}(V)         \ar@{->>}[r]^{\det}            \ar@{->>}[d]  & F^*                                                   \ar@{->>}[d] \\    \mathrm{PSL}(V)        \ar@{^(->}[r]  & \mathrm{PGL}(V)        \ar@{->>}[r]  & F^*/(F^*)^n }  $$}}} % end math, end frame \end{document} 

Licensing

Nils R. Barth, the copyright holder of this work, hereby publishes it under the following license:
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

7 May 2009

image/svg+xml

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current18:19, 7 May 2009Thumbnail for version as of 18:19, 7 May 2009491 × 254 (70 KB)Nbarth{{Information |Description = {{en|Commutative diagram showing the projective linear groups (special and general) and their relations }} |Source=Own work, created as per: [[:en:meta:Help:Displayin

The following page uses this file:

Global file usage

The following other wikis use this file: