✦ LIBER ✦

Laplacian and Homology of Free Two-Step Nilpotent Lie Algebras

✍ Scribed by Stefan Sigg

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 245 KB
Volume: 185
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0317

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✦ Synopsis

In this paper we determine the homology with trivial coefficients of the free two-step nilpotent Lie algebras over the complex numbers. This is done by working out the structure of the homology as a module under the general linear group. The main tool is a Laplacian for the free two-step nilpotent Lie algebras, which turns out to be closely related to the Casimir operator of the general linear group. We are able to compute all eigenvalues of the Laplacian on the chain complex.