The action of various operations on the cohomology of nilpotent Lie algebras is studied. In the cohomology of any Lie algebra, we show that the existence of certain nontrivial compositions of higher cohomology operations implies the existence of hypercube-like structures in cohomology, which in turn establishes the Toral Rank Conjecture for that Lie algebra. We provide examples in low dimensions and exhibit an infinite family of nilpotent Lie algebras of arbitrary dimension for which such structures exist. A new proof of the Toral Rank Conjecture is also given for free two-step nilpotent Lie algebras.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OOU-OLD./23623 |
| Date | 09 January 2013 |
| Creators | Amelotte, Steven |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thèse / Thesis |
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