论文标题
最大类型$ p $的最大级别的谎言代数
Graded Lie algebras of maximal class of type $p$
论文作者
论文摘要
标题的代数为无限维级谎言代数$ l = \ bigoplus_ {i = 1}^{\ infty} l_i $，在一个积极特征$ p $的领域，这些领域由$ 1 $ $ 1 $的元素和$ p $ $ p $ $ $ p $的元素和满足$ i i i i i i i i i i i; P $。如果$ p = 2 $此类代数在2003年被Caranti和Vaughan-Lee分类。我们宣布将该分类扩展到任意主要特征，并证明其证明的几个重大步骤。
The algebras of the title are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i$, over a field of positive characteristic $p$, that are generated by an element of degree $1$ and an element of degree $p$, and satisfy $[L_i,L_1]=L_{i+1}$ for $i\ge p$. In case $p=2$ such algebras were classified by Caranti and Vaughan-Lee in 2003. We announce an extension of that classification to arbitrary prime characteristic, and prove several major steps in its proof.
