Comments on a paper by Ceballos, Nunez, and Tenorio. Issue 2 (12th November 2020)

• Record Type: Journal Article
• Authors: Ghanam, Ryad; Thompson, Gerard
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 2(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-11-12
• Subjects: complex and real nilpotent Lie algebra -- minimal dimension matrix representation -- six and seven dimensions; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1132
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract: This article points out some of the shortcomings of a paper by Ceballos et al. In particular, representations of the indecomposable six‐dimensional complex nilpotent Lie algebras are corrected. In addition, the class of representations is extended so as to include all the indecomposable six‐dimensional real nilpotent Lie algebras. A test case is studied in detail in which it is shown that there is no representation of one of the six‐dimensional real nilpotent Lie algebras using 5 × 5 matrices. This test case points up some of the severe difficulties that one will encounter when implementing an algorithm such as the one developed by Ceballos et al. The case of the seven‐dimensional complex nilpotent Lie algebras is briefly touched upon and several representations are corrected.