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.
@article{10_37236_10821,
author = {Vincent E. Coll Jr. and Nicholas W. Mayers and Nicholas Russoniello},
title = {Contact {Lie} poset algebras},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {3},
doi = {10.37236/10821},
zbl = {1520.17008},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10821/}
}
TY - JOUR
AU - Vincent E. Coll Jr.
AU - Nicholas W. Mayers
AU - Nicholas Russoniello
TI - Contact Lie poset algebras
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/10821/
DO - 10.37236/10821
ID - 10_37236_10821
ER -
%0 Journal Article
%A Vincent E. Coll Jr.
%A Nicholas W. Mayers
%A Nicholas Russoniello
%T Contact Lie poset algebras
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10821/
%R 10.37236/10821
%F 10_37236_10821
Vincent E. Coll Jr.; Nicholas W. Mayers; Nicholas Russoniello. Contact Lie poset algebras. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10821
