Location of Repository

No-cycle algebras and representation theory

By Paul Boddington


In the first half of this dissertation we study certain quotient algebras of preprojective\ud algebras called no-cycle algebras N. These are studied via one-cycle algebras,\ud which are introduced here. Results include detailed combinatorial information on\ud N, and in certain special cases a presentation for N as a quiver with relations.\ud In the second half we consider deformations of coordinate algebras of\ud Kleinian singularities. Results include an explicit presentation for the deformations\ud of a type D singularity.\ud These two themes are tied together at the end by some mainly speculative\ud comments about the role the various objects studied have to play in representation\ud theory

Topics: QA
OAI identifier: oai:wrap.warwick.ac.uk:3482

Suggested articles



  1. (1990). A Class of Algebras Similar to the Enveloping Algebra Of 5 (2, doi
  2. (1994). An Introduction to Homological Algebra, Cambridge Studies doi
  3. (1982). Associative algebras, Graduate Texts doi
  4. (2001). Block repesentation type of reduced enveloping algebras,
  5. (1981). Cartan matrices, finite groups of quaternions, and Kleinian singulanties, doi
  6. (1999). Centres of reduced enveloping algebras, doi
  7. (1954). Finite Unitary Reflection Groups, doi
  8. Groups et Alg├Żbras de Lie, (Eight chapters in four separate volumes),
  9. (1996). Hilbert schemes and simple singularities, New Trends in Algebraic Geometry doi
  10. (1972). Lie Algebras, doi
  11. (1991). Linear Algebraic Groups, Graduate Texts doi
  12. (1981). Methods of Representation Theory Volume /,
  13. (1979). Model algebras and representations of graphs, doi
  14. (1998). Noncommutative deformations of Kleiman singulanties, doi
  15. (1937). On the Regular Representations of Algebras, doi
  16. (1976). Ordinary and Modular Representations of Chevalley Groups, doi
  17. (1993). Polynomial invariants of finite doi
  18. (1995). Polynomial invariants of finite groups, doi
  19. (1990). Reflection Groups and Coxeter Groups, Cambridge Studies doi
  20. (1997). Representations of Lie algebras in prime characteristic, doi
  21. (1999). Serni-Affine Coxeter-Dynkin Graphs and GC SU2(C), doi
  22. (1980). SIMple Singularities and SIMple Algebraic Groups, doi
  23. Singular Elements of Sernisimple Algebraic Groups, Actes Congres Intem.
  24. (1997). Special Transverse Slices and their Enveloping algebras, doi
  25. (1999). Subregular m1potent representations of sl, and S02n+l,
  26. (1999). Subregular nilpotent elements and bases in K-theory, doi
  27. (1999). Subregular nilpotent representations of Lie algebras in prime characteristic, doi
  28. (1993). Subregular Representations of M, and Simple Singularities of Type A,, -,,
  29. (1980). The preprojective algebra of a modulated graph. In: Representation theory //, doi
  30. (1987). The preprojective algebra of a tame hereditary algebra, doi
  31. (2001). The ramification of centres: Lie algebras in positive characteristic and quantised enveloping algebras, doi
  32. (1989). Two-dimensional tame and maximal orders of finite representation type, doi
  33. (1972). Unzerlegbare Darstellungen 1, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.