File:Hopf algebra.svg

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Original file(SVG file, nominally 185 × 166 pixels, file size: 30 KB)

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Summary

Description
English: A commutative hexagon expressing all the axioms of a Hopf algebra.
Date
Source Own work
Author Ryan Reich
Other versions File:HopfAlgebra.png

Source code

\documentclass{article}
\usepackage{amsmath,amssymb,nopageno}
\usepackage[all]{xy}
\DeclareMathOperator{\id}{id}
\begin{document}
 \begin{equation*}
  \xymatrix@C-1.5em@R+2em{
  & {H \otimes H} \ar[rr]^{S \otimes \id} & & {H \otimes H} \ar[dr]^{\nabla} & \\
  {H} \ar[ur]^{\Delta} \ar[dr]_{\Delta} \ar[rr]^{\varepsilon} & & {K} \ar[rr]^{\eta} & & {H} \\
  & {H \otimes H} \ar[rr]_{\id \otimes S} & & {H \otimes H} \ar[ur]_{\nabla} &
  }
 \end{equation*}
\end{document}

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
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I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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29 April 2009

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Date/TimeThumbnailDimensionsUserComment
current21:58, 29 April 2009Thumbnail for version as of 21:58, 29 April 2009185 × 166 (30 KB)wikimediacommons>Ryan Reich{{Information |Description={{en|1=A commutative hexagon expressing all the axioms of a Hopf algebra.}} |Source=Own work by uploader |Author=Ryan Reich |Date=2009-04-29 |Permission= |other_versions=File:HopfAlgebra.png }} == Source

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