Boddington, Paul (2004) No-cycle algebras and representation theory. PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Algebras, Linear, Algebraic cycles, Combinatorial analysis, Directed graphs, Projective modules (Algebra)
Date:	September 2004
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Rumynin, Dmitriy
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC)
Extent:	vi, 103 leaves
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/3482

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