Identities in the enveloping algebras for modular Lie superalgebras (Q1183279)

Let \(L=L_0\oplus L_1\) be a restricted Lie superalgebra over a field of positive characteristic \(p>2\). The author gives a sufficient and necessary condition for the existence of polynomial identities for the restricted universal enveloping algebra \(u(L)\). This result is refined when \(u(L)\) satisfies an identity of given degree. When the base field is algebraically closed of characteristic \(p>2\) the methods of the paper are applied to find conditions on a Lie superalgebra \(L\) equivalent to the property that all irreducible \(L\)-representations are bounded by a finite constant.