Edited by Lidia Angeleri Hügel
Edited by Dieter Happel
Edited by Henning Krause
Publisher: Cambridge University Press
Print Publication Year: 2007
Online Publication Date:May 2010
Online ISBN:9780511735134
Paperback ISBN:9780521680455
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511735134.016
Subjects: Algebra, Geometry and Topology
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The project to produce a Handbook of Tilting Theory was discussed during the Fraueninsel Conference 20 Years of Tilting Theory, in November 2002. A need was felt to make available surveys on the basic properties of tilting modules, tilting complexes and tilting functors, to collect outlines of the relationship to similar constructions in algebra and geometry, as well as reports on the growing number of generalizations. At the time the Handbook was conceived, there was a general consensus about the overall frame of tilting theory, with the tilted algebra as the core, surrounded by a lot of additional considerations and with many applications in algebra and geometry. One was still looking forward to further generalizations (say something like “pre-semi-tilting procedures for near-rings“), but the core of tilting theory seemed to be in a final shape. The Handbook was supposed to provide a full account of the theory as it was known at that time. The editors of this Handbook have to be highly praised for what they have achieved. But the omissions which were necessary in order to bound the size of the volume clearly indicate that there should be a second volume.
Part 1 will provide an outline of this core of tilting theory. Part 2 will then be devoted to topics where tilting modules and tilted algebras have sown to be relevant.
pp. i-iv
pp. v-viii
pp. 1-8
2 - Basic results of classical tilting theory : Read PDF
pp. 9-14
3 - Classification of representation-finite algebras and their modules : Read PDF
pp. 15-30
4 - A spectral sequence analysis of classical tilting functors : Read PDF
pp. 31-48
5 - Derived categories and tilting : Read PDF
pp. 49-104
6 - Hereditary categories : Read PDF
pp. 105-146
7 - Fourier-Mukai transforms : Read PDF
pp. 147-178
8 - Tilting theory and homologically finite subcategories with applications to quasihereditary algebras : Read PDF
pp. 179-214
9 - Tilting modules for algebraic groups and finite dimensional algebras : Read PDF
pp. 215-258
10 - Combinatorial aspects of the set of tilting modules : Read PDF
pp. 259-278
11 - Infinite dimensional tilting modules and cotorsion pairs : Read PDF
pp. 279-322
12 - Infinite dimensional tilting modules over finite dimensional algebras : Read PDF
pp. 323-344
13 - Cotilting dualities : Read PDF
pp. 345-358
14 - Representations of finite groups and tilting : Read PDF
pp. 359-392
15 - Morita theory in stable homotopy theory : Read PDF
pp. 393-412
Appendix: Some remarks concerning tilting modules and tilted algebras. Origin. Relevance. Future. : Read PDF
pp. 413-472