The Experts below are selected from a list of 66 Experts worldwide ranked by ideXlab platform

Jan Minac - One of the best experts on this subject based on the ideXlab platform.

  • freyd s Generating Hypothesis for groups with periodic cohomology
    Canadian Mathematical Bulletin, 2012
    Co-Authors: Sunil K Chebolu, Daniel J Christensen, Jan Minac
    Abstract:

    Let be a finite group, and let be a field whose characteristic divides the order of . Freyd's Generating Hypothesis for the stable module category of is the statement that a map between finite-dimensional -modules in the thick subcategory generated by factors through a projective if the induced map on Tate cohomology is trivial. We show that if has periodic cohomology, then the Generating Hypothesis holds if and only if the Sylow -subgroup of is or . We also give some other conditions that are equivalent to the for groups with periodic cohomology.

  • freyd s Generating Hypothesis with almost split sequences
    Proceedings of the American Mathematical Society, 2009
    Co-Authors: Jon F Carlson, Sunil K Chebolu, Jan Minac
    Abstract:

    Freyd's Generating Hypothesis for the stable module category of a non-trivial finite group G is the statement that a map between finitely generated kG-modules that belongs to the thick subcategory generated by the field k factors through a projective module if the induced map on Tate cohomology is trivial. In this paper we show that Freyd's Generating Hypothesis fails for kG when the Sylow p-subgroup of G has order at least 4 using almost split sequences. By combining this with our earlier work, we obtain a complete answer to Freyd's Generating Hypothesis for the stable module category of a finite group. We also derive some consequences of the Generating Hypothesis.

  • freyd s Generating Hypothesis with almost split sequences
    arXiv: Representation Theory, 2008
    Co-Authors: Jon F Carlson, Sunil K Chebolu, Jan Minac
    Abstract:

    Freyd's Generating Hypothesis for the stable module category of a non-trivial finite group G is the statement that a map between finitely generated kG-modules that belongs to the thick subcategory generated by k factors through a projective if the induced map on Tate cohomology is trivial. In this paper we show that Freyd's Generating Hypothesis fails for kG when the Sylow p-subgroup of G has order at least 4 using almost split sequences. By combining this with our earlier work, we obtain a complete answer to Freyd's Generating Hypothesis for the stable module category of a finite group. We also derive some consequences of the Generating Hypothesis.

  • the Generating Hypothesis for the stable module category of a p group
    arXiv: Representation Theory, 2006
    Co-Authors: David J Benson, Sunil K Chebolu, Daniel J Christensen, Jan Minac
    Abstract:

    Freyd's Generating Hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd's Generating Hypothesis holds for a non-trivial finite p-group G if and only if G is either C_2 or C_3. We also give various conditions which are equivalent to the Generating Hypothesis.

Sunil K Chebolu - One of the best experts on this subject based on the ideXlab platform.

  • freyd s Generating Hypothesis for groups with periodic cohomology
    Canadian Mathematical Bulletin, 2012
    Co-Authors: Sunil K Chebolu, Daniel J Christensen, Jan Minac
    Abstract:

    Let be a finite group, and let be a field whose characteristic divides the order of . Freyd's Generating Hypothesis for the stable module category of is the statement that a map between finite-dimensional -modules in the thick subcategory generated by factors through a projective if the induced map on Tate cohomology is trivial. We show that if has periodic cohomology, then the Generating Hypothesis holds if and only if the Sylow -subgroup of is or . We also give some other conditions that are equivalent to the for groups with periodic cohomology.

  • freyd s Generating Hypothesis with almost split sequences
    Proceedings of the American Mathematical Society, 2009
    Co-Authors: Jon F Carlson, Sunil K Chebolu, Jan Minac
    Abstract:

    Freyd's Generating Hypothesis for the stable module category of a non-trivial finite group G is the statement that a map between finitely generated kG-modules that belongs to the thick subcategory generated by the field k factors through a projective module if the induced map on Tate cohomology is trivial. In this paper we show that Freyd's Generating Hypothesis fails for kG when the Sylow p-subgroup of G has order at least 4 using almost split sequences. By combining this with our earlier work, we obtain a complete answer to Freyd's Generating Hypothesis for the stable module category of a finite group. We also derive some consequences of the Generating Hypothesis.

  • freyd s Generating Hypothesis with almost split sequences
    arXiv: Representation Theory, 2008
    Co-Authors: Jon F Carlson, Sunil K Chebolu, Jan Minac
    Abstract:

    Freyd's Generating Hypothesis for the stable module category of a non-trivial finite group G is the statement that a map between finitely generated kG-modules that belongs to the thick subcategory generated by k factors through a projective if the induced map on Tate cohomology is trivial. In this paper we show that Freyd's Generating Hypothesis fails for kG when the Sylow p-subgroup of G has order at least 4 using almost split sequences. By combining this with our earlier work, we obtain a complete answer to Freyd's Generating Hypothesis for the stable module category of a finite group. We also derive some consequences of the Generating Hypothesis.

  • the Generating Hypothesis for the stable module category of a p group
    arXiv: Representation Theory, 2006
    Co-Authors: David J Benson, Sunil K Chebolu, Daniel J Christensen, Jan Minac
    Abstract:

    Freyd's Generating Hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd's Generating Hypothesis holds for a non-trivial finite p-group G if and only if G is either C_2 or C_3. We also give various conditions which are equivalent to the Generating Hypothesis.

Jon F Carlson - One of the best experts on this subject based on the ideXlab platform.

  • freyd s Generating Hypothesis with almost split sequences
    Proceedings of the American Mathematical Society, 2009
    Co-Authors: Jon F Carlson, Sunil K Chebolu, Jan Minac
    Abstract:

    Freyd's Generating Hypothesis for the stable module category of a non-trivial finite group G is the statement that a map between finitely generated kG-modules that belongs to the thick subcategory generated by the field k factors through a projective module if the induced map on Tate cohomology is trivial. In this paper we show that Freyd's Generating Hypothesis fails for kG when the Sylow p-subgroup of G has order at least 4 using almost split sequences. By combining this with our earlier work, we obtain a complete answer to Freyd's Generating Hypothesis for the stable module category of a finite group. We also derive some consequences of the Generating Hypothesis.

  • freyd s Generating Hypothesis with almost split sequences
    arXiv: Representation Theory, 2008
    Co-Authors: Jon F Carlson, Sunil K Chebolu, Jan Minac
    Abstract:

    Freyd's Generating Hypothesis for the stable module category of a non-trivial finite group G is the statement that a map between finitely generated kG-modules that belongs to the thick subcategory generated by k factors through a projective if the induced map on Tate cohomology is trivial. In this paper we show that Freyd's Generating Hypothesis fails for kG when the Sylow p-subgroup of G has order at least 4 using almost split sequences. By combining this with our earlier work, we obtain a complete answer to Freyd's Generating Hypothesis for the stable module category of a finite group. We also derive some consequences of the Generating Hypothesis.

Mark Hovey - One of the best experts on this subject based on the ideXlab platform.

  • on freyd s Generating Hypothesis
    Quarterly Journal of Mathematics, 2007
    Co-Authors: Mark Hovey
    Abstract:

    Freyd's Generating Hypothesis in stable homotopy theory is revisited and new consequences and equivalent forms of it are derived. A surprising such consequence is that I, the Brown?Comenetz dual of the sphere and the source of many counterexamples in stable homotopy, is the cofibre of a self-map of a wedge of spheres. It is also shown that a consequence of the Generating Hypothesis, that the homotopy of a finite spectrum that is not a wedge of spheres can never be finitely generated as a module over *S, is in fact true for many finite torsion spectra.

  • the Generating Hypothesis in the derived category of a ring
    Mathematische Zeitschrift, 2007
    Co-Authors: Mark Hovey, Keir Lockridge, Gena Puninski
    Abstract:

    We show that a strong form (the fully faithful version) of the Generating Hypothesis, introduced by Freyd in algebraic topology, holds in the derived category of a ring R if and only if R is von Neumann regular. This extends results of the second author (J. Pure Appl. Algebra 208(2), 2007). We also characterize rings for which the original form (the faithful version) of the Generating Hypothesis holds in the derived category of R. These must be close to von Neumann regular in a precise sense, and, given any of a number of finiteness hypotheses, must be von Neumann regular. However, we construct an example of such a ring that is not von Neumann regular and therefore does not satisfy the strong form of the Generating Hypothesis.

  • the Generating Hypothesis in the derived category of a ring
    arXiv: Algebraic Topology, 2006
    Co-Authors: Mark Hovey, Keir Lockridge, Gena Puninski
    Abstract:

    We show that a strong form (the fully faithful version) of the Generating Hypothesis, introduced by Freyd in algebraic topology, holds in the derived category of a ring R if and only if R is von Neumann regular. This extends results of the second author. We also characterize rings for which the original form (the faithful version) of the Generating Hypothesis holds in the derived category of R. These must be close to von Neumann regular in a precise sense, and, given any of a number of finiteness hypotheses, must be von Neumann regular. However, we construct an example of such a ring that is not von Neumann regular, and therefore does not satisfy the strong form of the Generating Hypothesis.

Keir Lockridge - One of the best experts on this subject based on the ideXlab platform.

  • the Generating Hypothesis in the derived category of a ring
    Mathematische Zeitschrift, 2007
    Co-Authors: Mark Hovey, Keir Lockridge, Gena Puninski
    Abstract:

    We show that a strong form (the fully faithful version) of the Generating Hypothesis, introduced by Freyd in algebraic topology, holds in the derived category of a ring R if and only if R is von Neumann regular. This extends results of the second author (J. Pure Appl. Algebra 208(2), 2007). We also characterize rings for which the original form (the faithful version) of the Generating Hypothesis holds in the derived category of R. These must be close to von Neumann regular in a precise sense, and, given any of a number of finiteness hypotheses, must be von Neumann regular. However, we construct an example of such a ring that is not von Neumann regular and therefore does not satisfy the strong form of the Generating Hypothesis.

  • the Generating Hypothesis in the derived category of a ring
    arXiv: Algebraic Topology, 2006
    Co-Authors: Mark Hovey, Keir Lockridge, Gena Puninski
    Abstract:

    We show that a strong form (the fully faithful version) of the Generating Hypothesis, introduced by Freyd in algebraic topology, holds in the derived category of a ring R if and only if R is von Neumann regular. This extends results of the second author. We also characterize rings for which the original form (the faithful version) of the Generating Hypothesis holds in the derived category of R. These must be close to von Neumann regular in a precise sense, and, given any of a number of finiteness hypotheses, must be von Neumann regular. However, we construct an example of such a ring that is not von Neumann regular, and therefore does not satisfy the strong form of the Generating Hypothesis.

  • the Generating Hypothesis in the derived category of r modules
    arXiv: Algebraic Topology, 2005
    Co-Authors: Keir Lockridge
    Abstract:

    In this paper, we prove a version of Freyd's Generating Hypothesis for triangulated categories: if D is a cocomplete triangulated category and S is an object in D whose endomorphism ring is graded commutative and concentrated in degree zero, then S generates (in the sense of Freyd) the thick subcategory determined by S if and only if the endomorphism ring of S is von Neumann regular. As a corollary, we obtain that the Generating Hypothesis is true in the derived category of a commutative ring R if and only if R is von Neumann regular. We also investigate alternative formulations of the Generating Hypothesis in the derived category. Finally, we give a characterization of the Noetherian stable homotopy categories in which the Generating Hypothesis is true.