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On finitely presented functors, Auslander algebras and almost split sequences
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Nogueira, Maria Teresa Anes Duarte (1986) On finitely presented functors, Auslander algebras and almost split sequences. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1447104~S15
Abstract
This thesis consists of two parts:
In Part A we study the category of finitely presented functors and use it to determine the representation type of the Auslander Algebra of Aq = K-algebra <z:zq = 0> , denoted Rq (K is a field). This is possible because the category of finitely generated modules over Rq, mod Rq , is equivalent to the category of finitely presented functors from (mod Aq)ᵒᵖ to Mod k. Part A finishes with the construction of the Auslander-Reiten quiver of Rq in case q = 3.
Part B deals with the construction of almost split sequences in the category mod° Δ of lattices over an R-order Δ , where R is a complete discrete rank 1 valuation ring.
In the first chapter of part B we give a description of some unpublished work by J. A. Green who permitted me to include it in this thesis. This work contains a method to construct a short exact sequence 0-> N-> E-> S-> 0 in a way which gives an explicit expression for the subfunctor Im( ,g) of ( ,S) , and shows that the construction of almost split sequences can be viewed as a particular case of this problem.
In the second chapter of part B we continue this work by deducing a "trace formula" which provides a practical way of dealing with a certain step of the construction of almost split sequences in mod° Δ. Then we consider the particular case where Δ is the group ring.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Functor theory, Algebra -- Research, Finite groups, Sequences (Mathematics) | ||||
| Official Date: | July 1986 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Green, J. A. (James Alexander) | ||||
| Sponsors: | Instituto Nacional de Investigação Científica (Portugal) | ||||
| Extent: | ii, 186 leaves | ||||
| Language: | eng |
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