Title Minimal faithful upper-triangular matrix representations for solvable Lie algebras
Authors CEBALLOS GONZÁLEZ, MANUEL, Nunez, J. , Tenorio, A. F.
External publication No
Scope Article
Nature Científica
JCR Quartile 1
SJR Quartile 2
JCR Impact 1.632
SJR Impact 0.938
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-84999791715&doi=10.1016%2fj.cam.2016.09.015&partnerID=40&md5=a3da31e895a045bb54900579023be5b0
Publication date 01/07/2017
ISI 000394067700028
Scopus Id 2-s2.0-84999791715
DOI 10.1016/j.cam.2016.09.015
Abstract 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 6, but also for some solvable Lie algebras of arbitrary dimension. (C) 2016 Elsevier B.V. All rights reserved.
Keywords Solvable Lie algebra; Faithful matrix representation; Minimal representation; Symbolic computation; Non-numerical algorithm
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