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Residual finiteness of color Lie superalgebras


Authors: Yu. A. Bahturin and M. V. Zaicev
Journal: Trans. Amer. Math. Soc. 337 (1993), 159-180
MSC: Primary 17A70; Secondary 17B70
MathSciNet review: 1087050
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Abstract: A (color) Lie superalgebra $ L$ over a field $ K$ of characteristic $ \ne 2, 3$ is called residually finite if any of its nonzero elements remains nonzero in a finite-dimensional homomorphic image of $ L$. In what follows we are looking for necessary and sufficient conditions under which all finitely generated Lie superalgebras satisfying a fixed system of identical relations are residually finite. In the case $ \operatorname{char}\;K = 0$ we show that a variety $ V$ satisfies this property if and only if $ V$ does not contain all center-by-metabelian algebras and every finitely generated algebra of $ V$ has nilpotent commutator subalgebra.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1087050-0
Article copyright: © Copyright 1993 American Mathematical Society