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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.

MSC:

17B01 Identities, free Lie (super)algebras
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
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