Contact Lie Poset Algebras - Coll Jr., Vincent E.; Mayers, Nicholas W.; Russoniello, Nicholas (The Electronic Journal of Combinatorics, 2022)
We provide a combinatorial recipe for constructing all posets of height at most two for which the corresponding type-A Lie poset algebra is contact. In the case that such posets are connected, a discrete Morse theory argument establishes that the posets’ simplicial realizations are contractible. It follows from a cohomological result of Coll and Gerstenhaber on Lie semi-direct products that the corresponding contact Lie algebras are absolutely rigid.