论文标题
具有满足多项式身份的派生的谎言代数的结构
The structure of Lie algebras with a derivation satisfying a polynomial identity
论文作者
论文摘要
我们证明了lie代数的nil弱结果在任意字段上承认派生，该字段满足给定的多项式身份$ r（t）= 0 $。对于多项式$ r = t^n-1 $，我们获得了lie代数的nil骨的结果，并承认订单$ n $的定期推导。如果$ p $不划分某个不变的$ρ_n$，我们在特征$ p $中找到了特征$ p $的最佳限制。我们对Shalev介绍的正整数$ n $的集合$ \ MATHCAL {n} _p $的新描述，该$ n $是特征性的$ p> 0 $的有限尺寸非核能lie elgebra的定期派生的顺序。最后，我们将结果推广到$ \ bbb z $以上。
We prove nilpotency results for Lie algebras over an arbitrary field admitting a derivation, which satisfies a given polynomial identity $r(t)=0$. For the polynomial $r=t^n-1$ we obtain results on the nilpotency of Lie algebras admitting a periodic derivation of order $n$. We find an optimal bound on the nilpotency class in characteristic $p$ if $p$ does not divide a certain invariant $ρ_n$. We give a new description of the set $\mathcal{N}_p$ of positive integers $n$, introduced by Shalev, which arise as the order of a periodic derivation of a finite-dimensional non-nilpotent Lie algebra in characteristic $p>0$. Finally we generalize the results to Lie rings over $\Bbb Z$.
