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• W35640847 abstract "In this thesis, we investigate thick subcategories for stable categories of certain Frobenius categories and for derived categories of hereditary abelian categories. Both types of categories arise in the representation theory of finite-dimensional algebras. There is a close relation between such stable categories and the derived categories of hereditary abelian categories. We show that this relation is well-behaved concerning thick subcategories. Then, we give a classification of the thick subcategories of Db(mod(A)) where A is a finite-dimensional hereditary algebra of finite or tame representation type. This enables us to classify the thick subcategories of algebraic triangulated categories with finitely many indecomposable objects and the thick subcategories of the stable module categories of an important class of selfinjective algebras of tame representation type. The classification is of a combinatorial nature and we emphasise combinatorial aspects such as counting and the lattice structure. Zusammenfassung. In dieser Doktorarbeit untersuchen wir die dicken Unterkategorien fur stabile Kategorien von gewissen Frobenius Kategorien und fur derivierte Kategorien von erblichen abelschen Kategorien. Beide Arten von Kategorien kommen in der Darstellungstheorie von endlich-dimensionalen Algebren vor. Es gibt einen engen Zusammenhang zwischen solchen stabilen Kategorien und den derivierten Kategorien von erblichen abelschen Kategorien. Wir zeigen, dass diese Beziehung vertraglich ist mit den dicken Unterkategorien. Dann klassifizieren wir die dicken Unterkategorien von Db(mod(A)), wobei A eine endlich-dimensionale erbliche Algebra vom endlichen oder vom zahmen Darstellungstyp ist. Dies versetzt uns in die Lage, die dicken Unterkategorien von algebraischen triangulierten Kategorien mit endlich vielen unzerlegbaren Objekten zu klassifizieren. Ebenso klassifizieren wir die dicken Unterkategorien einer wichtigen Klasse von selbst-injektiven Algebren vom zahmen Darstellungstyp. Die Klassifikation ist kombinatorischer Natur und wir legen besonderen Wert auf kombinatorische Aspekte wie Zahlen und die Verbandsstruktur. Acknowledgements. First and foremost I wish to express my thanks to my supervisor, Professor Henning Krause. I thank him for his support, for helpful discussions and for coming up with the interesting topic of this thesis. I have created important parts of the thesis during my research stay in Paris with Professor Bernhard Keller in spring 2010. I sincerely thank him for giving me this opportunity, and for his very profitable assistance during this time. I would also like to thank the members and the visitors of the Paderborn Representation Theory Group and the Bielefeld Representation Theory Group for helpful discussions. I am particularly grateful to Professor Hideto Asashiba, Estanislao Herscovich, Dirk Kussin, Adam-Christiaan van Roosmalen, Greg Stevenson, Jan Stovicek and Dieter Vossieck. Moreover, I thank Philipp Lampe and Greg Stevenson for proofreading parts of the thesis. I would like to thank Martin Rubey for helpful references. Finally, I am indebted to the IRTG ‘Geometry and Analysis of Symmetries’ in Paderborn for the financial support in form of a scholarship. I am also grateful to the CRC 701 ‘Spectral Structures and Topological Methods in Mathematics’ in Bielefeld for the financial support during the final period of my PhD studies." @default.
• W35640847 created "2016-06-24" @default.
• W35640847 creator A5063392238 @default.
• W35640847 date "2011-01-01" @default.
• W35640847 modified "2023-09-24" @default.
• W35640847 title "A combinatorial classification of thick subcategories of derived and stable categories" @default.
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