On the homology of graded Lie algebras
β Scribed by Paulo Tirao
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 101 KB
- Volume
- 156
- Category
- Article
- ISSN
- 0022-4049
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β¦ Synopsis
We consider the homology of ΓΏnite-dimensional-graded Lie algebras with coe cients in a ΓΏnite-dimensional-graded module. By a combinatorial approach we give a lower bound for their total homology. Our result extends a result of Deninger and Singhof for the case of trivial coe cients. Applications for 2-step and free nilpotent Lie algebras are given.
π SIMILAR VOLUMES
Let (L; @) be a di erential graded Lie algebra over the prime ΓΏeld Fp. There exists an isomorphism of Hopf algebras H \* (UL) βΌ = UE, where E is a graded Lie algebra (J. Pure. Appl. Algebra 83 (1992) 237-282). Suppose that L is q-reduced for some q ΒΏ 1. We prove a generalization of a classical theor
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 this work large families of naturally graded nilpotent Lie algebras in arbitrary dimension and characteristic sequence (n; q; 1) with n β‘ 1(mod 2) satisfying the centralizer property are given. This centralizer property constitutes a generalization, for any nilpotent algebra, of the structural pr