Shirokov realizations of low dimensional Lie algebras

Severin Pošta

Shirokov realizations of low dimensional Lie algebras

Mathematical Physics 2026-06-26 v1 Representation Theory

Authors: Severin Pošta

Abstract

We compute the transitive realizations for the low dimensional cases of real Lie algebras up to dimension four using Shirokov's method. First, the generic realizations are given, then, making use of the known list of subalgebras, nongeneric realizations are computed. The result is compared with the known classification of Popovych et al.

Keywords

lie algebras shirokov realizations transitive realizations subalgebras low-dimensional

Cite

@article{arxiv.2606.28140,
  title  = {Shirokov realizations of low dimensional Lie algebras},
  author = {Severin Pošta},
  journal= {arXiv preprint arXiv:2606.28140},
  year   = {2026}
}

Comments

28 pages