In the first half of this dissertation we study certain quotient algebras of preprojective algebras called no-cycle algebras N. These are studied via one-cycle algebras, which are introduced here. Results include detailed combinatorial information on N, and in certain special cases a presentation for N as a quiver with relations. In the second half we consider deformations of coordinate algebras of Kleinian singularities. Results include an explicit presentation for the deformations of a type D singularity. These two themes are tied together at the end by some mainly speculative comments about the role the various objects studied have to play in representation theory.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:416141 |
| Date | January 2004 |
| Creators | Boddington, Paul |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/3482/ |
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