Representations of six-dimensional Mubarakazyanov Lie algebras (Q491316)

\textit{G. M. Mubarakzyanov} proposed in [Izv. Vyssh. Uchebn. Zaved., Mat. 1963, No. 4(35), 104--116 (1963; Zbl 0166.04202)] a classification of the real, solvable, indecomposable Lie algebra of dimension \(6\), whose nilradical has dimension \(5\). The first and the last author of the paper under review have recently issued a revised version of this classification, correcting a number of errors [J. Lie Theory 23, No. 2, 313--355 (2013; Zbl 1280.17014)]. In the paper under review, compact forms of (faithful) matrix representations of these algebras are given. There is an effective version of Ado's theorem by \textit{W. A. de Graaf} [in: Proceedings of the 1997 international symposium on symbolic and algebraic computation, ISSAC '97, Maui, HI, USA, July 21--23, 1997. New York, NY: ACM Press, 54--59 (1997; Zbl 0957.17001)], but the bounds on the dimension are quite large. In this case, it turns out that all of these algebras have matrix representations in degree \(6\). Combining this with other results from the literature [\textit{R. Ghanam} et al., Extr. Math. 20, No. 2, 151--184 (2005; Zbl 1146.22017); Hadronic J. 29, No. 3, 299--317 (2006; Zbl 1146.17304)], [\textit{M. Rawashdeh} and \textit{G. Thompson}, J. Math. Phys. 47, No. 11, 112901, 29 p. (2006; Zbl 1112.17033)], one obtains that all the \(6\)-dimensional real algebras have a matrix representation in degree \(6\).