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

SICILIANO, Salvatore
2006

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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