The algebraic classification of nilpotent commutative algebras
Doston JumaniyozovNational University of Uzbekistan, Tashkent, Uzbekistan, Institute of Mathematics named after V.I. Romanovsky Academy of Sciences of Uzbekistan, Tashkent, UzbekistanIvan KaygorodovCMCC, Universidade Federal do ABC, Santo André, Brazil, Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia, Saint Petersburg University, RussiaAbror KhudoyberdiyevNational University of Uzbekistan, Tashkent, Uzbekistan, Institute of Mathematics named after V.I. Romanovsky, Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan
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<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.
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