A Noncommutative Catenoid
Noncommutative geometry generalizes many geometric results from such fields as differential geometry and algebraic geometry to a context where commutativity cannot be assumed. Unfortunately there are few concrete non-trivial examples of noncommutative objects. The aim of this thesis is to construct a...
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| Format: | Others |
| Language: | English |
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Linköpings universitet, Matematik och tillämpad matematik
2017
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| Online Access: | http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-139794 |
| Summary: | Noncommutative geometry generalizes many geometric results from such fields as differential geometry and algebraic geometry to a context where commutativity cannot be assumed. Unfortunately there are few concrete non-trivial examples of noncommutative objects. The aim of this thesis is to construct a noncommutative surface <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathcal%7BC%7D_%5Chbar" /> which will be a generalization of the well known surface called the catenoid. This surface will be constructed using the Diamond lemma, derivations will be constructed over <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathcal%7BC%7D_%5Chbar" /> and a general localization will be provided using the Ore condition. |
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