We will extend the conjugacy problem of maximal toral subalgebras for Lie algebras of the form $\g{g} \otimes_k R$ by considering $R=k[t,t^{-1}]$ and $R=k[t,t^{-1},(t-1)^{-1}]$, where $k$ is an algebraically closed field of characteristic zero and $\g{g}$ is a direct limit Lie algebra. In the process, we study properties of infinite matrices with entries in a B\'zout domain and we also look at how our conjugacy results extend to universal central extensions of the suitable direct limit Lie algebras.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/26086 |
| Date | January 2013 |
| Creators | Gontcharov, Aleksandr |
| Contributors | Salmasian, Hadi |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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