• d-abelian quotients of (d+2)-angulated categories 

      Jacobsen, Karin Marie; Jørgensen, Peter (Journal article; Peer reviewed, 2019)
      Let T be a triangulated category. If t is a cluster tilting object and I=add t is the ideal of morphisms factoring through an object of add t, then the quotient category T/I is abelian. This is an important result of cluster ...
    • Existence of a 2-cluster tilting module does not imply finite complexity. 

      Vaso, Laertis; Marczinzik, René (Journal article, 2022)
      We give an example of a finite-dimensional algebra with a 2-cluster tilting module and a simple module which has infinite complexity. This answers a question of Erdmann and Holm.
    • Maximal τ_d-rigid pairs 

      Jacobsen, Karin Marie; Jørgensen, Peter (Journal article; Peer reviewed, 2020)
      Let C be a 2-Calabi–Yau triangulated category, T a cluster tilting object with endomorphism algebra Γ. Consider the functor C(T,-): C -> mod Γ. It induces a bijection from the isomorphism classes of cluster tilting objects ...
    • Minimal semi-flat-cotorsion replacements and cosupport 

      Nakamura, Tsutomu; Thompson, Peder (Journal article; Peer reviewed, 2020)
      Over a commutative noetherian ring Rof finite Krull dimension, we show that every complex of flat cotorsion R-modules decomposes as a direct sum of a minimal complex and a contractible complex. Moreover, we define the ...
    • 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 ...
    • A refinement of Gorenstein flat dimension via the flat--cotorsion theory 

      Christensen, Lars Winther; Estrada, Sergio; Liang, Li; Thompson, Peder; Wu, Dejun; Yang, Gang (Peer reviewed; Journal article, 2021)
      We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of ...
    • Tau-exceptional sequences 

      Buan, Aslak Bakke; Marsh, Bethany Rose (Journal article; Peer reviewed, 2021)
      We introduce the notions of τ-exceptional and signed τ-exceptional sequences for any finite dimensional algebra. We prove that for a fixed algebra of rank n, and for any positive integer , there is a bijection between ...
    • The third Milgram--Priddy class lifts 

      Szymik, Markus (Peer reviewed; Journal article, 2020)
      Abstract: We show that the third cohomology of the finite general linear group with trivial mod 2 coefficients is non-zero. The necessarily unique non-trivial element restricts to the third Milgram–Priddy class.