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\begin{document}

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\section*{Yangian}

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{related_concepts}{Related Concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak


\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

A \emph{Yangian} is a certain [[quantum group]] that arises naturally in [[integrable systems]] in [[quantum field theory]], as well as in \emph{[[semi-holomorphic 4d Chern-Simons theory]]}.

\hypertarget{related_concepts}{}\subsection*{{Related Concepts}}\label{related_concepts}

\begin{itemize}%
\item [[quantum affine algebra]]

\end{itemize}
\hypertarget{references}{}\subsection*{{References}}\label{references}

\begin{itemize}%
\item Wikipedia, \emph{\href{http://en.wikipedia.org/wiki/Yangian}{Yangian}}


\item A. I. Molev, \emph{Yangians and their applications}, in ``Handbook of Algebra'' vol. \textbf{3} (M. Hazewinkel, Ed.), Elsevier 2003, 907-959 \href{http://arxiv.org/abs/math/0211288}{math.QA/0211288}; \emph{Yangians and classical Lie algebras}, AMS Math. Surv. Monog. \textbf{143}, 2007; 400 pp; Russian edition: \emph{    }, , , 2009


\item N. J. Mackay, \emph{Introduction to Yangian symmetry in integrable field theory} (\href{http://arxiv.org/abs/hep-th/0409183}{arXiv:hep-th/0409183})


\item [[Vassili Gorbounov]], R. Rimanyi, V. Tarasov, A. Varchenko, \emph{Cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra} (\href{http://arxiv.org/abs/1204.5138}{arXiv:1204.5138})


\item V. G. [[Drinfeld]], \emph{Degenerate affine Hecke algebras and Yangians}, Funct. Anal. Appl. 20 (1986), 58--60.


\item Denis Uglov, \emph{Symmetric functions and the Yangian decomposition of the Fock and basic modules of the affine Lie algebra $\mathfrak{sl}^N$}, Math. Soc. Japan Memoirs \textbf{1}, 1998, 183-241 \href{http://projecteuclid.org/euclid.msjm/1389985795}{euclid} \href{http://dx.doi.org/10.2969/msjmemoirs/00101C030}{doi}


\item A. N. Kirillov, N. Y. Reshetikhin, \emph{The Yangians, Bethe Ansatz and combinatorics}, Lett. Math. Phys. \textbf{12}, 199 (1986)


\item Sachin Gautam, Valerio Toledano-Laredo, \emph{Yangians and quantum loop algebras}, Selecta Mathematica \textbf{19} (2013), 271-336 \href{http://arxiv.org/abs/1012.3687}{arxiv/1012.3687}; \emph{II. Equivalence of categories via abelian difference equations} \href{http://arxiv.org/abs/1310.7318}{arxiv/1310.7318}; \emph{III. Meromorphic equivalence of tensor structures} \href{http://arxiv.org/abs/1403.5251}{arxiv/1403.5251}



\end{itemize}
Review in the context of [[AdS-CFT]] includes

\begin{itemize}%
\item [[Alessandro Torrielli]], \emph{Yangians, S-matrices and AdS/CFT}, J.Phys.A44:263001,2011 (\href{http://arxiv.org/abs/1104.2474}{arXiv:1104.2474})

\end{itemize}
In

\begin{itemize}%
\item [[Kevin Costello]], \emph{Supersymmetric gauge theory and the Yangian} (\href{http://arxiv.org/abs/1303.2632}{arXiv:1303.2632})

\end{itemize}
is discussed that the holomorphically [[topological twist|twisted]] [[N=1 D=4 super Yang-Mills theory]] is controled by the [[Yangian]] in analogy to how [[Chern-Simons theory]] is controled by a [[quantum group]]. See at \emph{[[semi-holomorphic 4d Chern-Simons theory]]}.

[[!redirects Yangians]]



\end{document}