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Title: Homological methods for graded k-Algebras
Author: Matthews, Brian
ISNI:       0000 0001 3621 4172
Awarding Body: University of Glasgow
Current Institution: University of Glasgow
Date of Award: 2007
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In this thesis we develop results concerning strongly group-graded lk-algebras. Chapter 1 is mainly expository: we set up a careful treatment of well-known facts and definitions regarding graded algebras so that later results run smoothly. A secondary reason for including the treatment is to give the reader a solid grounding in the basics: much use will be made of these initial observations throughout the thesis. In Chapter 2 we establish generalisations of known work for group algebras. Here the paper Complexity and Varieties for infinite groups, I by D. J. Benson is key, with results of J. Cornick and P. H. Kropholler discussed and generalised as needed. The main theorems of this chapter characterise - albeit under specific conditions - modules of finite projective dimension over strongly group-graded lk-algebras for G an LH~-group. Chapter 3 sees us take a different tack with complete cohomology where we define the zeroeth cohomology group to be the set of morphisms in certain module categories. We show that these categories can be realised as quotients of the derived category of suitable subcategories. This work also generalises results due to Benson. We introduce some vanishing theorems for modules of type FP 00 over skew polynomial rings, with suitable finiteness conditions on the base ring in Chapter 4. Iterated skew polynomial rings are also investigated, as are iterated skew Laurent polynomial rings.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics