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作者:David J. Benson , Jon F. Carlson
来源:[J].Journal of Algebra(IF 0.583), 2019
摘要:Abstract(#br)We introduce the concept of a nearly null map in the stable module category, and relate it to the notion of virtual projectivity. We show that the trivial module k is virtually M -projective if and only if the map f : N → k in the triangle N → f k ...
作者:Riccardo Colpi , Francesca Mantese , Alberto Tonolo
来源:[J].Journal of Pure and Applied Algebra(IF 0.534), 2011, Vol.215 (12), pp.2923-2936
摘要:Abstract(#br)An abelian category with arbitrary coproducts and a small projective generator is equivalent to a module category (Mitchell (1964)[17]). A tilting object in an abelian category is a natural generalization of a small projective generator. Moreover, any abelian category...
作者:Ioannis Emmanouil
来源:[J].Journal of Algebra(IF 0.583), 2017, Vol.478, pp.174-194
摘要:Abstract(#br)We show that any module admits a presentation as the quotient of a Gorenstein projective module by a submodule which is itself right orthogonal, with respect to the standard Ext 1 pairing, to the class of Gorenstein projective modules of type FP ∞ . For that purpo...
作者:Jonathan Cornick , Ioannis Emmanouil , Peter Kropholler ...
来源:[J].Advances in Mathematics(IF 1.373), 2014, Vol.260, pp.375-400
摘要:... To that end, we determine the structure of completely finitary Gorenstein projective modules over group rings. The methods are inspired by representation theory and make use of the stable module category, in which morphisms are defined through complete cohomology. In order...
作者:Nicolás Andruskiewitsch , Juan Martín Mombelli
来源:[J].Journal of Algebra(IF 0.583), 2007, Vol.314 (1), pp.383-418
摘要:Abstract(#br)We show that indecomposable exact module categories over the category Rep H of representations of a finite-dimensional Hopf algebra H are classified by left comodule algebras, H -simple from the right and with trivial coinvariants, up to equivariant Morita equival...
作者:Gilles Ph Gnacadja
来源:[J].Journal of Algebra(IF 0.583), 1998, Vol.201 (2), pp.686-702
摘要:Abstract(#br)We study phantom maps in the stable module category StMod ( kG ), where k is a field and G is a finite group. In this article we almost exclusively deal with maps out of countably generated modules. We show that the space Ph kG ( M , N ) of stabilized phantom m...
作者:Lidia Angeleri Hügel , Jan Šaroch , Jan Trlifaj
来源:[J].Journal of Pure and Applied Algebra(IF 0.534), 2007, Vol.212 (2), pp.297-310
摘要:... 68 (2003) 631–650], the Telescope Conjecture was formulated for the module category Mod R of an artin algebra R as follows: “If C = ( A , B ) is a complete hereditary cotorsion pair in Mod R with A and B ...
作者:Dave Benson , Srikanth B. Iyengar , Henning Krause ...
来源:[J].Journal of the American Mathematical Society(IF 3.567), 2017, Vol.31 (1), pp.265-302
摘要:The tensor ideal localizing subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning the structure of the stable module category...
作者:Shawn Baland , Alexandru Chirvasitu , Greg Stevenson
来源:[J].Transactions of the American Mathematical Society(IF 1.019), 2018, Vol.371 (1), pp.489-503
摘要:For a finite group $ G$ and an arbitrary commutative ring $ R$, Broué has placed a Frobenius exact structure on the category of finitely generated $ RG$-modules by taking the exact sequences to be those that split upon restriction to the trivial subgroup. The corresponding s...
作者:Gregor Schaumann
来源:[J].Journal of Algebra(IF 0.583), 2013, Vol.379, pp.382-425
摘要:Abstract(#br)We consider traces on module categories over pivotal fusion categories which are compatible with the module structure. It is shown that such module traces characterise the Morita classes of special haploid Frobenius algebras. Moreover, they are unique up to a scale f...

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