The Thick Subcategory Generated by the Trivial Module

2000 ◽  
pp. 285-296
Author(s):  
Jon F. Carlson
Keyword(s):  
Trivial Module ◽  
Thick Subcategory

Ghosts and Strong Ghosts in the Stable Category

2016 ◽  
Vol 59 (4) ◽  
pp. 682-692
Author(s):  
Jon F. Carlson ◽  
Sunil K. Chebolu ◽  
Ján Mináč
Keyword(s):  
Finite Group ◽  
Strong Form ◽  
Finite Range ◽  
Finitely Generated ◽  
Stable Category ◽  
Tate Cohomology ◽  
Trivial Module ◽  
A Finite Group ◽  
Thick Subcategory ◽  
Generating Hypothesis

AbstractSuppose that G is a finite group and k is a field of characteristic p > 0. A ghost map is a map in the stable category of finitely generated kG-modules which induces the zero map in Tate cohomology in all degrees. In an earlier paper we showed that the thick subcategory generated by the trivial module has no nonzero ghost maps if and only if the Sylow p-subgroup of G is cyclic of order 2 or 3. In this paper we introduce and study variations of ghost maps. In particular, we consider the behavior of ghost maps under restriction and induction functors. We find all groups satisfying a strong form of Freyd’s generating hypothesis and show that ghosts can be detected on a finite range of degrees of Tate cohomology. We also consider maps that mimic ghosts in high degrees.

scholarly journals Localisation and colocalisation of triangulated categories at thick subcategories

2012 ◽  
Vol 110 (1) ◽  
pp. 59 ◽  
Author(s):  
Hvedri Inassaridze ◽  
Tamaz Kandelaki ◽  
Ralf Meyer
Keyword(s):  
Exact Sequence ◽  
Triangulated Category ◽  
Triangulated Categories ◽  
Canonical Map ◽  
Derived Functor ◽  
Homological Functor ◽  
Thick Subcategory

Given a thick subcategory of a triangulated category, we define a colocalisation and a natural long exact sequence that involves the original category and its localisation and colocalisation at the subcategory. Similarly, we construct a natural long exact sequence containing the canonical map between a homological functor and its total derived functor with respect to a thick subcategory.

scholarly journals GENERIC JORDAN TYPE OF THE SYMMETRIC AND EXTERIOR POWERS

2014 ◽  
Vol 13 (05) ◽  
pp. 1350163 ◽  
Author(s):  
DAVID J. BENSON ◽  
KAY JIN LIM
Keyword(s):  
Jordan Type ◽  
Trivial Module ◽  
Exterior Powers

We prove a result relating the stable generic Jordan types of the symmetric and exterior powers of the Heller translations of a module for a finite elementary abelian p-group. In the case of the trivial module, the stable generic Jordan types of the symmetric and exterior powers of its Heller translations are completely described.

scholarly journals A thick subcategory theorem for modules over certain ring spectra

2015 ◽  
Vol 19 (4) ◽  
pp. 2359-2392 ◽  
Author(s):  
Akhil Mathew
Keyword(s):  
Ring Spectra ◽  
Thick Subcategory

scholarly journals The MCM-approximation of the trivial module over a category algebra

2017 ◽  
Vol 16 (06) ◽  
pp. 1750109 ◽  
Author(s):  
Ren Wang
Keyword(s):  
Projective Modules ◽  
Ground Field ◽  
Stable Category ◽  
Gorenstein Projective Modules ◽  
Tensor Identity ◽  
Trivial Module

For a finite free EI category, we construct an explicit module over its category algebra. If in addition the category is projective over the ground field, the constructed module is a maximal Cohen–Macaulay approximation of the trivial module and is the tensor identity of the stable category of Gorenstein-projective modules over the category algebra. We give conditions on when the trivial module is Gorenstein-projective.

scholarly journals Cohomology of simple modules for sl3(k) in characteristic 3

2021 ◽  
Vol 103 (3) ◽  
pp. 36-43
Author(s):  
A.A. Ibrayeva ◽  
Keyword(s):  
Algebraic Group ◽  
Lie Algebra ◽  
Quotient Algebra ◽  
Characteristic P ◽  
One Dimensional ◽  
Simple Modules ◽  
Trivial Module ◽  
Characteristic 3 ◽  
Simple Quotient ◽  
Classical Lie Algebra

In this paper we calculate cohomology of a classical Lie algebra of type A2 over an algebraically field k of characteristic p = 3 with coefficients in simple modules. To describe their structure we will consider them as modules over an algebraic group SL3(k). In the case of characteristic p = 3, there are only two peculiar simple modules: a simple that module isomorphic to the quotient module of the adjoint module by the center, and a one-dimensional trivial module. The results on the cohomology of simple nontrivial module are used for calculating the cohomology of the adjoint module. We also calculate cohomology of the simple quotient algebra Lie of A2 by the center.

Trivial module for ortho-symplectic Lie superalgebras and Littlewood’s formula

2012 ◽  
Vol 56 (11) ◽  
pp. 2251-2260
Author(s):  
BinTao Cao ◽  
Li Luo
Keyword(s):  
Lie Superalgebras ◽  
Trivial Module

Homology and Cohomology of the Super Schrödinger Algebra S(1/1) with Coefficients in the Trivial Module

2019 ◽  
Vol 26 (04) ◽  
pp. 615-628
Author(s):  
Yan He ◽  
Yuezhu Wu ◽  
Linsheng Zhu
Keyword(s):  
Cohomology Groups ◽  
Homology Groups ◽  
Dimensional Spacetime ◽  
Trivial Module ◽  
Schrödinger Algebra

In this paper we study the homology and cohomology groups of the super Schrödinger algebra [Formula: see text] in (1 + 1)-dimensional spacetime. We explicitly compute the homology groups of [Formula: see text] with coefficients in the trivial module. Then using duality, we finally obtain the dimensions of the cohomology groups of [Formula: see text] with coefficients in the trivial module.

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