On the structure of the cohomology of nilpotent Lie algebras
The exterior algebra over the centre of a Lie algebra acts on the cohomology of the Lie algebra in a natural way. Focusing on nilpotent Lie algebras, we explore the module structure afforded by this action. We show that for all two-step nilpotent Lie algebras, this module structure is non-trivial, w...
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| Format: | Others |
| Language: | en |
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University of Ottawa (Canada)
2013
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| Online Access: | http://hdl.handle.net/10393/28015 http://dx.doi.org/10.20381/ruor-19039 |
| Summary: | The exterior algebra over the centre of a Lie algebra acts on the cohomology of the Lie algebra in a natural way. Focusing on nilpotent Lie algebras, we explore the module structure afforded by this action. We show that for all two-step nilpotent Lie algebras, this module structure is non-trivial, which partially answers a conjecture of Cairns and Jessup [4]. The presence of free submodules indicates that the Lie algebra satisfies Halperin's Toral rank conjecture [11]. We prove that two specific classes of two-step nilpotent Lie algebras enjoy cohomology spaces with free submodules. |
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