A classification of localizing subcategories by relative homological algebra

Nadareishvili, George

dc.contributor.advisor	Meyer, Ralf Prof. Dr.
dc.contributor.author	Nadareishvili, George
dc.date.accessioned	2015-12-17T10:10:25Z
dc.date.available	2015-12-17T10:10:25Z
dc.date.issued	2015-12-17
dc.identifier.uri	http://hdl.handle.net/11858/00-1735-0000-0028-867A-A
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-5429
dc.language.iso	eng	de
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc	510	de
dc.title	A classification of localizing subcategories by relative homological algebra	de
dc.type	doctoralThesis	de
dc.contributor.referee	Meyer, Ralf Prof. Dr.
dc.date.examination	2015-10-16
dc.description.abstracteng	In this thesis, we use the tools of relative homological algebra in triangulated categories to define a sensible notion of support for objects in the bootstrap class of a Kasparov category of C-algebras over a finite topological space with totally ordered lattice of open subsets. This category is equivalent to a bootstrap category of filtrations of C-algebras. As a consequence, we provide a full classification of localizing subcategories of the bootstrap category in terms of a product of lattices of noncrossing partitions of a regular polygon. In addition, we consider the 2-periodic derived category of countable modules over the ring of upper triangular matrices. Since the homological algebra is the same, the lattices of localizing subcategories in this category and the bootstrap category are isomorphic.	de
dc.contributor.coReferee	Schick, Thomas Prof. Dr.
dc.subject.eng	C*-algebra	de
dc.subject.eng	Kasparov category	de
dc.subject.eng	homological algebra	de
dc.subject.eng	triangulated category	de
dc.subject.eng	non-commutative topology	de
dc.subject.eng	filtrations of C*-algebras	de
dc.subject.eng	C*-algebras over a topological space	de
dc.subject.eng	localizing subcategory	de
dc.subject.eng	localising subcategory	de
dc.subject.eng	Bivariant K-theory	de
dc.subject.eng	Filtrated K-theory	de
dc.subject.eng	relative homological algebra	de
dc.subject.eng	bootstrap class	de
dc.subject.eng	KK-theory	de
dc.subject.eng	ring of upper triangular matrices	de
dc.identifier.urn	urn:nbn:de:gbv:7-11858/00-1735-0000-0028-867A-A-3
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	Mathematics (PPN61756535X)	de
dc.identifier.ppn	844401765

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