Betti number of nilpotent Lie algebras and graph ideals

Abstract

It is shown that, how spectral sequence arguments can contribute to a solution in a concrete setting. For one-dimensional extensions of a Heisenberg algebra, we determine the Betti numbers exactly and then show that some families in this class have a M-shaped Betti number distribution, and construct the first examples with an even more exotic complete bipartite graph which are independent of choice of field. Finally, we discuss the Betti numbers for the star graph with [Formula: see text] vertices.