, Volume 196, Issue 1, pp 161-173

Lie superalgebras whose enveloping algebras satisfy a non-matrix polynomial identity

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Abstract

Let L be a Lie superalgebra with its enveloping algebra U(L) over a field F. A polynomial identity is called non-matrix if it is not satisfied by the algebra of 2×2 matrices over F. We characterize L when U(L) satisfies a non-matrix polynomial identity. We also characterize L when U(L) is Lie solvable, Lie nilpotent, or Lie super-nilpotent.

The research of the second author was supported by NSERC of Canada.
The third author was supported by NSERC and MITACS.