The algebraic classification of nilpotent commutative algebras

Abstract

<p style='text-indent:20px;'>This paper is devoted to the complete algebraic classification of complex <inline-formula><tex-math id="M1">\begin{document}$ 5 $\end{document}</tex-math></inline-formula>-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller nilpotent commutative algebras and the recently obtained classification of complex <inline-formula><tex-math id="M2">\begin{document}$ 5 $\end{document}</tex-math></inline-formula>-dimensional nilpotent commutative <inline-formula><tex-math id="M3">\begin{document}$ \mathfrak{CD} $\end{document}</tex-math></inline-formula>-algebras.</p>