File:Hopf algebra.svg

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

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Category:Self-published work#Hopf%20algebra.svgCategory:PD-self#Hopf%20algebra.svg Category:SVG commutative diagrams Category:Images with LaTeX source code
Category:Images with LaTeX source code Category:PD-self Category:SVG commutative diagrams Category:Self-published work