Enveloping algebras of restricted Lie superalgebras satisfying non-matrix polynomial identities

Details Enveloping algebras of restricted Lie superalgebras satisfying non-matrix polynomial identities Enveloping algebras of restricted Lie superalgebras satisfying non-matrix polynomial identities

2009-10-15

arxiv.org/abs/0910.2977v2

Mathematics

Rings and Algebras

proofs of some of the statements are shortened along with transparent ideas, some typos are fixed

Scientific paper

Let L be a restricted Lie superalgebra with its enveloping algebra u(L) over a field F of characteristic p>2. A polynomial identity is called non-matrix if it is not satisfied by the algebra of 2\times 2 matrices over F. We characterize L when u(L) satisfies a non-matrix polynomial identity. In particular, we characterize L when u(L) is Lie solvable, Lie nilpotent, or Lie super-nilpotent.

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