On toral posets and contact Lie algebras (Q6107810)

Lie subalgebras of \(sl(n)\) which lie between Cartan subalgebras and associated Borel subalgebras are called type-A Lie poset algebras. Using combinatorial arguments, \textit{V. E. Coll jun.} et al. [Electron. J. Comb. 29, No. 3, Research Paper P3.35, 22 p. (2022; Zbl 1520.17008)] gave a complete characterization of those posets with chains of cardinality at most three whose associated type-A Lie posets are contact. In the present work, the authors generate toral posets, with chains of arbitrary size, associated to contact type-A Lie poset algebras. They conjecture that all contact, type-A Lie poset algebras are either associated to posets of this form or associated to a direct sum of posets of this form.