English

Classical orthogonal decomposition of a modular $\mathfrak{sl}_n$

Rings and Algebras 2024-07-08 v1

Abstract

An orthogonal decomposition problem of Lie algebras over the complex numbers has been studied since the 1980s. It has many applications and relations to other areas of mathematics and sciences. In this paper, we consider this decomposition problem over a field of prime characteristic. We define a classical orthogonal decomposition of a modular Lie algebra and construct it for sln\mathfrak{sl}_n under certain sufficient conditions. Additionally, we provide more detailed analysis of the problem when n=2n = 2 and 33.

Keywords

Cite

@article{arxiv.2407.03367,
  title  = {Classical orthogonal decomposition of a modular $\mathfrak{sl}_n$},
  author = {Yotsanan Meemark and Songpon Sriwongsa},
  journal= {arXiv preprint arXiv:2407.03367},
  year   = {2024}
}

Comments

In this arXiv version, we correct the conclusion about the uniqueness of COD of $\mathfrak{sl}_3$ in Section 3 of the published version. Moreover, we provide the input for one part of Appendix A, making the Mathematica Code more accessible to readers

R2 v1 2026-06-28T17:28:21.189Z