Operators in the cohomology of nilpotent Lie algebras.

dc.contributor.advisor	Jessup, Barry
dc.contributor.author	LeBel, Alain Claude.
dc.date.accessioned	2009-04-17T16:01:48Z
dc.date.available	2009-04-17T16:01:48Z
dc.date.created	2001
dc.date.issued	2001
dc.degree.level	Masters
dc.degree.name	M.Sc.
dc.description.abstract	Operators in the cohomology of Lie algebras are defined, and fundamental results are proven. The central representation is shown to be useful, in particular cases, for proving the Toral Rank Conjecture (TRC), which states the logarithm of the total dimension of any nilpotent Lie algebra's cohomology space is greater than or equal to the dimension of the centre. Central representation and secondary operators are used to find hypercube-like structures in the cohomology of the free two-step nilpotent Lie algebras with two, three and four generators. Also, a theorem about the new operators acting on the cohomology of the Heisenberg Lie algebras, and how these operators interact with Poincare duality for this case, is proven.
dc.format.extent	88 p.
dc.identifier.citation	Source: Masters Abstracts International, Volume: 45-06, page: 3172.
dc.identifier.uri	http://hdl.handle.net/10393/10775
dc.identifier.uri	http://dx.doi.org/10.20381/ruor-8446
dc.publisher	University of Ottawa (Canada)
dc.subject.classification	Mathematics.
dc.title	Operators in the cohomology of nilpotent Lie algebras.
dc.type	Thesis

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