Blar i Institutt for matematiske fag på forfatter "Oppermann, Steffen"
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An Introduction To Triangulated Categories
Thorbjørnsen, Thomas Wilskow (Bachelor thesis, 2021)Denne bacheloroppgaven har som mål i å gi en presentasjon av teorien til triangulerte kategorier. Hovedmålet er å vise at Verdier kvotientent, homotopikategorien og den deriverte kategorien er triangulert. -
Change of rings and singularity categories
Oppermann, Steffen; Psaroudakis, Chrysostomos; Stai, Torkil Utvik (Journal article, 2019)We investigate the behavior of singularity categories and stable categories of Gorenstein projective modules along a morphism of rings. The natural context to approach the problem is via change of rings, that is, the ... -
Cluster equivalence and graded derived equivalence
Amiot, Claire; Oppermann, Steffen (Peer reviewed; Journal article, 2014)In this paper we introduce a new approach for organizing algebras of global dimension at most 2. We introduce the notion of cluster equivalence for these algebras, based on whether their generalized cluster categories are ... -
Derived equivalence classification techniques for Nakayama algebras
Fosse, Didrik (Doctoral theses at NTNU;2024:18, Doctoral thesis, 2024)In the representation theory of finite dimensional algebras, the fundamental goal is to understand the structure of the category mod⇤ of finite dimensional modules over an algebra ⇤. While solving this problem is difficult ... -
Gentle Algebras and a Geometric Model for the Module Category
Sjøborg, Christina Dønvold (Master thesis, 2021)I denne oppgaven viser vi at milde algebraer er isomorfe til flisalgebraer. Flisalgebraer kan visulaiseres som en lamineringsalgebra, som brukes til å gjenopprette den milde algebraen. Disse isomorfiene danner grunnlaget ... -
Hochschild cohomology, monoidal categories and quantum complete intersections
Hellstrøm-Finnsen, Magnus (Doctoral theses at NTNU;2018:6, Doctoral thesis, 2018) -
On cluster-tilting modules for some symmetric algebras
Kringeland, Tor (Master thesis, 2020)Klassifisering av kluster-vipping-modular til nokre symmetriske algebraar -
On orbit and localization constructions for triangulated categories
Stai, Torkil Utvik (Doctoral theses at NTNU;2017:224, Doctoral thesis, 2017) -
On the Derived Category of Strongly Homotopy Associative Algebras
Thorbjørnsen, Thomas Wilskow (Master thesis, 2022)I denne avhandlingen studerer vi homotopiteorien til assosiative dg-algebraer, konilpotente koassosiative dg-koalgebraer og sterkt homotopi-assosiative algebraer. Vi bruker vridde morfier for å vise at kobar-bar konstruksjonen ... -
Partial Serre duality and cocompact objects
Oppermann, Steffen; Psaroudakis, Chrysostomos; Stai, Torkil Utvik (Journal article, 2023) -
Proving Wedderburn's little theorem
Olaisen, Emil August Hovd (Bachelor thesis, 2020)Oppgaven handler om å bevise Wedderburn's lille teorem som sier at et hvert endelig integritetsområde er en endelig kropp. Oppgaven begynner med å bevise at endelige integritets områder er divisjonsringer. Etter det beskrives ... -
Realization functors and HRS-tilting
Malkenes, Johannes (Master thesis, 2021)La A vær en abelsk kategori, og H vær det abelske hjertet til en t-struktur over Db(A). Vi vil da vise at vi alltid kan konstruere en "realization functor" Db(H) -> Db(A), som restriktert til H vil være lik identitetsfun ... -
Relating abelian categories to triangulated categories using generalized cluster tilting methods
Grimeland, Benedikte (Doctoral thesis at NTNU;2016:75, Doctoral thesis, 2016) -
Representation Theory of Geigle-Lenzing Complete Intersections
Herschend, Martin; Iyama, Osamu; Minamoto, Hiroyuki; Oppermann, Steffen (Journal article, 2023) -
Rickard's Morita theorem for derived categories
Fosse, Didrik (Master thesis, 2019)Vi gir, i full detalj, to ulike bevis for Rickards moritateorem for deriverte kategorier. I det første beviset bruker vi et modifisert dobbeltkjedekompleks for å konstruere en ekvivalens mellom de deriverte kategoriene ... -
Subcategory structures, Grothendieck groups and higher homological algebra
Haugland, Johanne (Doctoral theses at NTNU;2023:113, Doctoral thesis, 2023) -
Tau-tilting Theory in Representation Theory of Finite Dimensional Algebras
Karlsen, Terje Bull (Master thesis, 2016)Tau-tilting theory was recently introduced by Adachi, Iyama and Reiten. Their main aim was to develop a generalization of classical tilting theory where mutation is always possible. The inspiration for this came mainly ... -
Tau-tilting Theory in Representation Theory of Finite Dimensional Algebras
Karlsen, Terje Bull (Master thesis, 2016)Tau-tilting theory was recently introduced by Adachi, Iyama and Reiten. Their main aim was to develop a generalization of classical tilting theory where mutation is always possible. The inspiration for this came mainly ... -
The Derived Category of Exact Categories and Classification of Exact Structures
Berre, Ole (Master thesis, 2021)I denne avhandlingen vil vi se på Verdier-lokalisering og asykliske komplekser for å kunne definere den deriverte kategorien. I tillegg finner vi en klassifisering av eksakte strukturer på idempotent komplette kategorier ...