The main goal of this paper is to compute a minimal matrix representation for each non-isomorphic nilpotent Lie algebra of dimension less than 6, Indeed, for each of these algebras, we search the natural number n e N {1} such that the linear algebra ft,,, formed by all the n x n complex strictly upper-triangular matrices, contains a representation of this algebra, Bes/des, we show an algorithmic procedure which computes such a minimal representation by using the Lie algebras ft,, In this way, a classification of such algebras according to the dimension of their minimal matrix representations is obtained. In this way, we improve some results by Burde related to the value of the minimal dimension of the matrix representations for nilpotent Lie algebras.
展开▼
机译：本文的主要目标是为维数小于6的每个非同构幂等李代数计算一个最小矩阵表示，实际上，对于这些代数中的每一个，我们搜索自然数ne N {1}使得线性由所有nxn严格上三角复数矩阵组成的代数ft包含该代数Bes / des的表示，我们展示了一种算法过程，该算法通过使用李代数ft计算这种最小表示，根据其最小矩阵表示的维数获得此类代数的分类。这样，我们通过Burde改进了一些与幂立李代数的矩阵表示的最小维值有关的结果。
展开▼
