Betti number behavior for nilpotent Lie algebras (Q881912)

The author uses spectral sequences to determine an explicit formula for the Betti numbers of one dimensional split extensions of a Heisenberg Lie algebra. The toral rank conjecture is also considered. This paper is essentially a list of examples and most of the proofs of statements are contained in two previous works, one of the author [Bull. Aust. Math. Soc. 71, No. 3, 459--470 (2005; Zbl 1162.17310)] and one of the author and \textit{P.~Tirao} [J. Algebra 292, No. 2, 585--591 (2005; Zbl 1086.17011)].