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
| 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. |