Faithful representations of Lie algebras and Homogeneous Spaces

2013/04/30 by Petros A. Terzis, Terzis, Petros A. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Representation Theory (math.RT) #gr-qc #math-ph #math.MP #math.RT

paper · pdf · doi:10.48550/arxiv.1304.7894

20 pages, no figures

openalex publication_date 2013/04/30 · arxiv created 2014/06/18 · arxiv updated 2014/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The faithful representations of real Lie algebras g with dimensions n≤ 4 acting on the dual space of the universal covering algebra of an ideal s of g, are calculated. With the help of left and right translations of the Lie group, we define the homogeneous manifolds of dimension n and we calculate the Killing fields (generators of left translations), the invariant fields (generators of right translations) and the left invariant 1-forms.

Cited by

• Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras

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