The Lie structure of enveloping algebras. (English) Zbl 0798.17011
The authors determine for precisely which Lie algebras \(L\) over fields of characteristic \(p>0\) the restricted universal enveloping algebra \(u(L)\) is Lie solvable (for \(p>2\)), Lie nilpotent, or satisfies the Engel condition. One of the consequences of these results is that Lie solvability is equivalent to Lie nilpotence in graded group rings of odd characteristic.
Reviewer: G.Brown (Boulder)
MSC:
17B50 | Modular Lie (super)algebras |
17B35 | Universal enveloping (super)algebras |
17B30 | Solvable, nilpotent (super)algebras |