Kabanov, A. N. The hypercentral structure of the group of unitriangular automorphisms of a free metabelian Lie algebra. (Russian, English) Zbl 1224.17011 Sib. Mat. Zh. 50, No. 2, 329-333 (2009); translation in Sib. Math. J. 50, No. 2, 261-264 (2009). Summary: We describe the hypercentral structure of the group of unitriangular automorphisms of a free metabelian Lie algebra over an arbitrary field. Using it, we prove that this group admits no faithful representation by matrices over a field provided that the algebra rank is at least four. Cited in 2 Documents MSC: 17B01 Identities, free Lie (super)algebras 17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras Keywords:metabelian Lie algebra; unitriangular automorphism; hypercenter; linearity PDFBibTeX XMLCite \textit{A. N. Kabanov}, Sib. Mat. Zh. 50, No. 2, 329--333 (2009; Zbl 1224.17011); translation in Sib. Math. J. 50, No. 2, 261--264 (2009) Full Text: EuDML EMIS