论文标题
SL（2，k）和非分类的三维简单谎言代数的参与
Involutions of sl(2,k) and non-split, three-dimensional simple Lie algebras
论文作者
论文摘要
我们提供了一个过程，可以根据SL（2，K）的参与来构建非分类，三维简单的谎言代数，其中k是一个特征的领域，而不是两个。到等效性，以这种方式获得的非分数三维简单谎言代数是由K的Brauer组的一个亚组进行了参数，其特征是它们的杀戮形式代表-2。在本地和全球领域，我们根据希尔伯特（Hilbert）和莱格德尔（Legendre）符号重新表达了这种条件，并给出了三维简单的谎言代数的例子，该代数可以并且无法通过这种构造在理性领域中获得。
We give a process to construct non-split, three-dimensional simple Lie algebras from involutions of sl(2,k), where k is a field of characteristic not two. Up to equivalence, non-split three-dimensional simple Lie algebras obtained in this way are parametrised by a subgroup of the Brauer group of k and are characterised by the fact that their Killing form represents -2. Over local and global fields we re-express this condition in terms of Hilbert and Legendre Symbols and give examples of three-dimensional simple Lie algebras which can and cannot be obtained by this construction over the field of rationals.
