论文标题
谎言结构和连锁理想晶格
Lie structures and chain ideal lattices
论文作者
论文摘要
本文的目的是双重的。首先，要强调，带有理想链晶格的谎言代数类是谎言代数的嵌入或分解，并具有有限的理想晶格。其次，表明该类别的谎言代数数量很大，并且它们支持其他类型的谎言结构。从一般示例和代数分解开始，我们专注于计算算法来构建谎言代数，其中理想的晶格是链条。链条条件会迫使该类代数的nilradicals上的等级。我们的算法产生了几个积极的自然级别级代数参数族。还将讨论进一步的概括和其他类型的结构。
The purpose of this paper is twofold. Firstly, to emphasise that the class of Lie algebras with chain lattices of ideals are elementary blocks in the embedding or decomposition of Lie algebras with finite lattice of ideals. Secondly, to show that the number of Lie algebras of this class is large and they support other types of Lie structures. Beginning with general examples and algebraic decompositions, we focus on computational algorithms to build Lie algebras in which the lattice of ideals is a chain. The chain condition forces gradings on the nilradicals of this class of algebras. Our algorithms yield to several positive naturally graded parametric families of Lie algebras. Further generalizations and other kind of structures will also be discussed.
