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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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 |
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ndltd-uottawa.ca-oai-ruor.uottawa.ca-10393-280152018-01-05T19:07:48Z On the structure of the cohomology of nilpotent Lie algebras Pestov, Sviatoslav Mathematics. 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. 2013-11-07T19:03:13Z 2013-11-07T19:03:13Z 2008 2008 Thesis Source: Masters Abstracts International, Volume: 48-01, page: 0430. http://hdl.handle.net/10393/28015 http://dx.doi.org/10.20381/ruor-19039 en 68 p. University of Ottawa (Canada) |
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NDLTD |
| language |
en |
| format |
Others
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| sources |
NDLTD |
| topic |
Mathematics. |
| spellingShingle |
Mathematics. Pestov, Sviatoslav On the structure of the cohomology of nilpotent Lie algebras |
| description |
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. |
| author |
Pestov, Sviatoslav |
| author_facet |
Pestov, Sviatoslav |
| author_sort |
Pestov, Sviatoslav |
| title |
On the structure of the cohomology of nilpotent Lie algebras |
| title_short |
On the structure of the cohomology of nilpotent Lie algebras |
| title_full |
On the structure of the cohomology of nilpotent Lie algebras |
| title_fullStr |
On the structure of the cohomology of nilpotent Lie algebras |
| title_full_unstemmed |
On the structure of the cohomology of nilpotent Lie algebras |
| title_sort |
on the structure of the cohomology of nilpotent lie algebras |
| publisher |
University of Ottawa (Canada) |
| publishDate |
2013 |
| url |
http://hdl.handle.net/10393/28015 http://dx.doi.org/10.20381/ruor-19039 |
| work_keys_str_mv |
AT pestovsviatoslav onthestructureofthecohomologyofnilpotentliealgebras |
| _version_ |
1718602476323602432 |