1. Minimal faithful upper-triangular matrix representations for solvable Lie algebras
- Author
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Juan Núñez, Manuel Ceballos, Ángel F. Tenorio, Universidad de Sevilla. Departamento de Geometría y Topología, Universidad de Sevilla. FQM326: Geometría Diferencial y Teoría de Lie, Ministerio de Economia, Industria y Competitividad (MINECO). España, and European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
- Subjects
Triangular matrix ,010103 numerical & computational mathematics ,01 natural sciences ,Graded Lie algebra ,Non-numerical algorithm ,Symbolic computation ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,FOS: Mathematics ,0101 mathematics ,Representation Theory (math.RT) ,Mathematics ,Faithful upper-triangular matrix representation ,Solvable Lie algebra ,Applied Mathematics ,010102 general mathematics ,Kac–Moody algebra ,Affine Lie algebra ,Lie conformal algebra ,Algebra ,Computational Mathematics ,Adjoint representation of a Lie algebra ,Fundamental representation ,17\, B\, 30, 17\, B\, 05, 17--08, 68W30, 68W05 ,Minimal representation ,Mathematics - Representation Theory - Abstract
A well-known result on Lie Theory states that every finite-dimensional complex solvable Lie algebra can be represented as a matrix Lie algebra, with upper-triangular square matrices as elements. However, this result does not specify which is the minimal order of the matrices involved in such representations. Hence, the main goal of this paper is to revisit and implement a method to compute both that minimal order and a matrix representative for a given solvable Lie algebra. As application of this procedure, we compute representatives for each solvable Lie algebra with dimension less than $6$., 19 pages, 6 tables
- Published
- 2017