Minimal faithful upper-triangular matrix representations for solvable Lie algebras

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• 作者：M. Ceballos^a ; ^{mceballos@uloyola.es} ; J. Nú ; ñ ; ez^b ; ^{jnvaldes@us.es} ; Á ; .F. Tenorio^c ; ^{aftenorio@upo.es}
• 关键词：17  ; B  ; 30 ; 17  ; B  ; 05 ; 17&ndash ; 08 ; 68W30 ; 68W05
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：279-292
• 全文大小：646 K
• 卷排序：318

文摘

The existence of matrix representations for any given finite-dimensional complex Lie algebra is a classic result on Lie Theory. In particular, such representations can be obtained by means of an isomorphic matrix Lie algebra consisting of upper-triangular square matrices. Unfortunately, there is no general information about the minimal order for the matrices involved in such representations. In this way, our main goal is to revisit, debug and implement an algorithm which provides the minimal order for matrix representations of any finite-dimensional solvable Lie algebra when inserting its law, as well as returning a matrix representative of such an algebra by using the minimal order previously computed. In order to show the applicability of this procedure, we have computed minimal representatives not only for each solvable Lie algebra with dimension less than 66, but also for some solvable Lie algebras of arbitrary dimension.