• Additive og subadditive funksjoner og Auslander-Reiten-quiver 

      Lyngroth, Sigurd Gjelsvik (Master thesis, 2016)
      I denne oppgaven studerer vi Cartanmatriser, additive og subadditive funksjoner og translasjonsquivre. Spesielt vil vi se hvordan additive og subadditive funksjoner er definert både for Cartanmatriser og for translasjonsquivre, ...
    • Analyse av varmegjenvinning og varmeutnyttelse i aluminiumsverk: Utnyttelse av spillvarme til forvarming av omsmeltemetall 

      Solberg, Øyvind (Master thesis, 2007)
      Hensikten med oppgaven var å redegjøre for mulighetene til å benytte seg av spillvarme fra holdeovnene i støperiet til forvarming av omsmeltemetall som ett ledd i å ta bruk spillvarmen ved bedriften. I den sammenheng ble ...
    • Auslander-Gorenstein algebras and precluster tilting 

      Iyama, Osamu; Solberg, Øyvind (Journal article; Peer reviewed, 2018)
      We generalize the notions of n-cluster tilting subcategories and τselfinjective algebras into n-precluster tilting subcategories and τn-selfinjective algebras, where we show that a subcategory naturally associated to ...
    • Auslander-Reiten components containing modules of finite complexity 

      Toft, Tea (Master thesis, 2011)
      Let R be a connected selfinjective Artin algebra. We prove that any almost split sequence ending at an Omega-perfect R-module of finite complexity has at most four non-projective summands in a chosen decomposition of the ...
    • Compactly Generated Triangulated Categories and the Telescope Conjecture 

      Stovicek, Jan (Doktoravhandlinger ved NTNU, 1503-8181; 2009:188, Doctoral thesis, 2009)
      The thesis studies the telescope conjecture for algebraic compactly generated triangulated categories. The conjecture, which says that every smashing localization of a compactly generated triangulated category is generated ...
    • Computing Almost Split Sequences: An algorithm for computing almost split sequences of finitely generated modules over a finite dimensional algebra 

      Lian, Tea Sormbroen (Master thesis, 2012)
      An artin algebra $l$ over a commutative, local, artinian ring $R$ was fixed, and with this foundation some topics from representation theory were discussed. A series of functors of module categories were defined, and almost ...
    • Computing tau-rigid modules 

      Terland, Håvard Utne (Master thesis, 2021)
      I denne masteroppgaven blir tau-vippeteori, som utviklet av Adachi, Iyama og Reiten i [AIR13], introdusert. Det blir så demonstrert hvordan teknikker fra [BST19] og kombinatoriske ideer kan anvendes i denne teorien. Vi ...
    • Decomposition of Modules over finite-dimensional Algebras 

      Haugland, Tormod (Master thesis, 2018)
      We investigate algorithms for decomposing a module $M$ over a finite-dimensional path algebra $\Lambda$. The algorithms first have to construct the endomorphism ring \[ \End(M) = \Hom(M, M). \] \noindent Consequently, ...
    • Finitistic Dimension Conjecture 

      Grevstad, Jacob Fjeld (Master thesis, 2021)
      I denne oppgaven oppsummerer vi arbeidet gjort på finitistisk dimensjonsformodning for endeligdimensjonale algebraer siden den først ble postulert i 1960. Vi fokuserer spesielt på å vise hvilke klasser av algebraer hvor ...
    • Going relative with Maurice—a survey 

      Solberg, Øyvind (Journal article, 2018)
    • Koszul Algebras and Linear Modules: An introduction to the theory of Koszul algebras and linear modules. 

      Friis, Pernille (Master thesis, 2010)
      In this thesis Koszul algebras and their modules, so called linear modules, are introduced. In order to do so, graded $K$-algebras, where $K$ is a field, are also defined and discussed. Furthermore, an isomorphism between ...
    • Koszul-algebraer over endelige kropper 

      Sundtjønn, Trude Pedersen (Master thesis, 2008)
      Vi har i denne masteroppgaven sett på Koszul-algebraer. Vi har definert Koszul-algebraer som graderte algebraer hvor de simple modulene har en lineær gradert projektiv oppløsning, og vi har bevist forskjellige karakteriseringer ...
    • Koszul-algebraer over endelige kropper 

      Olsen, Kari-Lise Frisvold (Master thesis, 2008)
      Masteroppgaven er innen algebra, nærmere bestemt Koszul-teori for algebraer. Koszul-algebraer, ble først definert av Priddy, har en sentral rolle innen algebra, geometri og topologi. Projektive moduler er viktige for å ...
    • On support varieties and tensor products for finite dimensional algebras 

      Bergh, Petter Andreas; Sandøy, Mads Hustad; Solberg, Øyvind (Peer reviewed; Journal article, 2020)
      It has been asked whether there is a version of the tensor product property for support varieties over finite dimensional algebras defined in terms of Hochschild cohomology. We show that in general no such version can ...
    • On the structure and cohomology ring of connected Hopf algebras 

      Erdmann, Karin; Solberg, Øyvind; Wang, Xingting (Peer reviewed; Journal article, 2019)
      Let p be a prime, and k be a field of characteristic p. We investigate the algebra structure and the structure of the cohomology ring for the connected Hopf algebras of dimension p3, which appear in the classification ...
    • Path Algebras of Coverings and Twisted Tensor Products 

      Unneland, Tobias Dysthe (Master thesis, 2015)
      The first part of the thesis introduces and discusses the twisted tensor product of two algebras. This is then used to show how the path algebra of a covering quiver relates to the quiver it is a covering of. In the end ...
    • Post-Quantum Multivariate Cryptography - A Study of Gui and GeMSS Signature Schemes using Gröbner Bases 

      Follan, Øyvind (Master thesis, 2018)
      The main goal of this thesis is to analyze and compare the two signature schemes Gui and GeMSS, both submitted to the Post-Quantum Cryptography Standardization Process initiated by the National Institute of Standards and ...
    • Quivers and admissible relations of tensor products and trivial extensions 

      Skartsæterhagen, Øystein Ingmar (Master thesis, 2011)
      We show how to find quotients of path algebras isomorphic to tensor products, triangular matrix algebras and trivial extensions.
    • Support Varieties for Finite Dimensional Algebras 

      Sandøy, Mads Hustad (Master thesis, 2016)
      We give a presentation of the theory of support varieties for finite dimensional algebras A using the Hochschild cohomology ring. Our presentation is especially focused on the finite generation hypotheses an algebra must ...
    • Support varieties—an axiomatic approach 

      Buan, Aslak Bakke; Krause, Henning; Snashall, Nicole; Solberg, Øyvind (Journal article; Peer reviewed, 2019)
      We provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category, where the tensor product is not necessarily symmetric. This is illustrated ...