Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 5 2 2024 03 01 An algebraic proof of the classification of five-dimensional nilsolitons 243 252 207805 10.30504/jims.2024.463565.1189 EN H. R. Salimi Moghaddam Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan. 0000-0001-6112-4259 Journal Article 2024 06 18 In 2002, using a variational method, Lauret classified five-dimensional nilsolitons. In this work, using the algebraic Ricci soliton equation, we obtain the same classification. We show that, among ten classes of five-dimensional connected and simply connected nilmanifolds, seven classes admit the Ricci soliton structure. In any case, the derivation which satisfies the algebraic Ricci soliton equation is computed. Ricci soliton left-invariant Riemannian metric nilsoliton five-dimensional nilmanifolds https://jims.ims.ir/article_207805_e8f9188db685d751d710fddcd80728ad.pdf