In this paper we examine the Lie derived length of a restricted universal enveloping algebra \$u(L)\$, where \$L\$ is a restricted Lie algebra over a field \$F\$ of characteristic \$p>0\$. In particular, we prove that, if the Lie derived length of \$u(L)\$ is at most \$n\$ and \$p\geq 2^n\$, then \$L\$ is abelian. Moreover, we establish when is a restricted universal enveloping algebra strongly Lie solvable and study its strong Lie derived length.

### Lie derived lengths of restricted universal enveloping algebras

#### Abstract

In this paper we examine the Lie derived length of a restricted universal enveloping algebra \$u(L)\$, where \$L\$ is a restricted Lie algebra over a field \$F\$ of characteristic \$p>0\$. In particular, we prove that, if the Lie derived length of \$u(L)\$ is at most \$n\$ and \$p\geq 2^n\$, then \$L\$ is abelian. Moreover, we establish when is a restricted universal enveloping algebra strongly Lie solvable and study its strong Lie derived length.
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Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/11587/107523`
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