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 L
The Moduli Space of Six-Dimensional Two-Step Nilpotent Lie Algebras
β Scribed by Sergio Console; Anna Fino; Evangelia Samiou
- Publisher
- Springer
- Year
- 2005
- Tongue
- English
- Weight
- 626 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0232-704X
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π SIMILAR VOLUMES
We find an explicit formula for the total dimension of the homology of a free 2-step nilpotent Lie algebra. We analyse the asymptotics of this formula and use it to find an improved lower bound on the total dimension of the homology of any 2-step nilpotent Lie algebra.
In the paper one- and two-dimensional cohomology is compared for finite and infinite nilpotent Lie algebras, with coefficients in the adjoint representation. It turns out that, because the adjoint representation is not a highest weight representation in infinite dimension, the considered cohomology
Let G 4 be the unique, connected, simply connected, four-dimensional, nilpotent Lie group. In this paper, the discrete cocompact subgroups H of G 4 are classified and shown to be in 1-1 correspondence with triples p 1 p 2 p 3 β 3 that satisfy p 2 p 3 > 0 and a certain restriction on p 1 . The K-grou