Laplacian and homology of free two-step nilpotent Lie algebras
The author determines the homology (with trivial coefficients) of the two-step nilpotent Lie algebra \({\mathbf m}_r:= {\mathbf f}_r/ C^3({\mathbf f}_r)\), where \({\mathbf f}_r\) is the free Lie algebra of rank \(r\) and \(C^3({\mathbf f}_r):= [{\mathbf f}_r,[{\mathbf f}_r,{\mathbf f}_r]]\), over the complex number field by working out the structure of the homology as a module of the general linear group. The article under review is a shortened version of the author's doctoral thesis under the title ``Laplace- Operator und Homologie von freien nilpotenten Lie Algebren der Klasse 2'', which was reviewed in Zbl 0854.17024.
scientific article; zbMATH DE number 941228