Betti number behavior for nilpotent Lie algebras
type: Item
instance of: scholarly article
title: Betti number behavior for nilpotent Lie algebras
zbMATH Open document ID: 1163.17022
author: Hannes Pouseele
published in: Geometriae Dedicata
publication date: 2007-05-18T00:00:00Z
review text: 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)].
reviewed by: Daniel Tanré
Mathematics Subject Classification ID: 17B56
zbMATH DE Number: 5154820
zbMATH Keywords: Lie algebra
zbMATH Keywords: cohomology
zbMATH Keywords: Betti numbers
zbMATH Keywords: Toral rank conjecture
MaRDI profile type: Publication
full work available at URL: s10711-005-9029-9
OpenAlex ID: W2005238385
cites work: Unimodal betti numbers for a class of nilpotent lie algebras
cites work: Explicit Betti numbers for a family of nilpotent Lie algebras
cites work: On the cohomology of a class of nilpotent Lie algebras
cites work: New bounds on the betti numbers of nilpotent lie algebras
cites work: On the cohomology of nilpotent Lie algebras
cites work: Q5850573
cites work: On the cohomology of extensions by a Heisenberg Lie algebra
cites work: Constructing Lie algebra homology classes
cites work: Cohomology of Heisenberg Lie Algebras
cites work: A refinement of the toral rank conjecture for 2-step nilpotent Lie algebras
DOI: 10.1007/S10711-005-9029-9
description: scientific article; zbMATH DE number 5154820