English

On toral posets and contact Lie algebras

Rings and Algebras 2023-06-14 v1 Combinatorics

Abstract

A (2k+1)(2k+1)-dimensional Lie algebra is called contact if it admits a one-form φ\varphi such that φ(dφ)k0.\varphi\wedge(d\varphi)^k\neq 0. Here, we extend recent work to describe a combinatorial procedure for generating contact, type-A Lie poset algebras whose associated posets have chains of arbitrary cardinality, and we conjecture that our construction leads to a complete characterization.

Keywords

Cite

@article{arxiv.2208.09060,
  title  = {On toral posets and contact Lie algebras},
  author = {Nicholas W. Mayers and Nicholas Russoniello},
  journal= {arXiv preprint arXiv:2208.09060},
  year   = {2023}
}