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Cohomology Operations and the Toral Rank Conjecture for Nilpotent Lie Algebras

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.

Identiferoai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/23623
Date January 2013
CreatorsAmelotte, Steven
ContributorsJessup, Barry
PublisherUniversité d'Ottawa / University of Ottawa
Source SetsUniversité d’Ottawa
LanguageEnglish
Detected LanguageEnglish
TypeThesis

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