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Noetherianness of wreath products of abelian Lie algebras with respect to equations of universal enveloping algebra. (Russian, English) Zbl 1164.17010

Algebra Logika 47, No. 4, 475-490 (2008); translation in Algebra Logic 47, No. 4, 269-278 (2008).
Summary: It is proved that the wreath product of two abelian finite-dimensional Lie algebras over a field of characteristic zero is Noetherian w.r.t. equations of a universal enveloping algebra. This implies that an index 2 soluble free Lie algebra of finite rankalso has this property.

MSC:

17B05 Structure theory for Lie algebras and superalgebras
17B01 Identities, free Lie (super)algebras
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