File:PSU-PU.svg

Summary

[edit]

Description

English: Commutative diagram, showing the unitary group.

Date

25 November 2007 (original upload date)

Source

Own work, created as per: Help:Displaying a formula: Commutative diagrams; source code below.

Author

Nils R. Barth

Permission
(Reusing this file)

Nils R. Barth, the copyright holder of this work, hereby publishes it under the following license:

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.

TeX source

[edit]

\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{ %Our diagram is a 3x3 matrix
\mathbf{Z}/n \ar@{^(->}[d]\ar@{^(->}[r]
  & U(1) \ar@{^(->}[d]\ar@{->>}[r]^{z^n}
  & U(1) \ar[d]^\wr\\
SU(n)    \ar@{->>}[d]\ar@{^(->}[r]
  & U(n) \ar@{->>}[d]\ar@{->>}[r]^{\det}
  & U(1)\\
PSU(n)   \ar[r]^\sim
  & PU(n)
}

$$}}} % end math, end frame
\end{document}

Original upload log

[edit]

The original description page was here. All following user names refer to en.wikipedia.

2007-11-25 20:55 Nbarth 394×253×0 (53021 bytes) Updated to increase default size.
2007-11-25 20:10 Nbarth 160×104×0 (50669 bytes) Updated to increase margin.
2007-11-25 19:46 Nbarth 145×93×0 (50906 bytes) Commutative diagram, showing the projective special unitary group and projective unitary group, presented as (sub)quotients the unitary group.

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TeX source

Original upload log

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