Related papers: Annihilators of simple tensor modules

Let R be a commutative noetherian ring. We prove that if R is either an equidimensional finitely generated algebra over a perfect field, or an equidimensional equicharacteristic complete local ring with a perfect residue field, then the…

In an attempt to get some information on the multiplicative structure of the Green ring we study algebraic modules for simple groups, and associated groups such as quasisimple and almost-simple groups. We prove that, for almost all groups…

It has been shown by McCoy that a right ideal of a polynomial ring with several indeterminates has a non-trivial homogeneous right annihilator of degree 0 provided its right annihilator is non-trivial to begin with. In this note, it is…

In this paper, we prove Faltings' annihilator theorem for complexes over a CM-excellent ring. As an application, we give a complete classification of the t-structures of the bounded derived category of finitely generated modules over a…

Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the…

We investigate finite non-Abelian simple groups $G$ for which the projective cover of the trivial module coincides with the permutation module on a subgroup and classify all cases unless $G$ is of Lie type in defining characteristic.

We consider the space of tensor densities on the n-dimensional sphere with degree lambda (or, equivalently, of conformal densities with degree lambda). This space is a module over the group of diffeomorphisms, and consequently over the Lie…

In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…

Suppose that $G$ is a finite group and $k$ is a field of characteristic $p >0$. Let $\mathcal{M}$ be the thick tensor ideal of finitely generated modules whose support variety is in a fixed subvariety $V$ of the projectivized prime ideal…

The simplicity of the induced modules for reductive Lie algebras over an algebraically closed field of positive characteristic is studied, and a necessary and sufficient condition for the simplicity is given.

We define a filtration indexed by the integers on the tensor product of an integrable highest weight module and a loop module for a quantum affine algebra. We prove that the filtration is either trivial or strictly decreasing and give…

We show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra $\tilde\goth g$ we construct the corresponding level $k$ vertex operator algebra and we show that level $k$ highest weight $\tilde\goth…

For an untwisted affine Lie algebra we prove an embedding of any higher level Demazure module into a tensor product of lower level Demazure modules (e.g. level one in type A) which becomes in the limit (for anti-dominant weights) the…

Recollements of derived module categories are investigated, using a new technique, ladders of recollements, which are mutation sequences. The position in the ladder is shown to control whether a recollement restricts from unbounded to…

We show that certain factor rings of the group algebra of a symmetric group have natural bases of group elements. We also give generators for the annihilator of certain permutation modules for symmetric groups.

We classify the localising tensor ideal and colocalising hom-closed subcategories of the stable module category for $\mathrm{LH}\mathfrak{F}$ groups. Along the way we develop techniques to provide similar classifications for other…

This paper is concerned with the tight closure of an ideal in a commutative Noetherian local ring $R$ of prime characteristic $p$. Several authors, including R. Fedder, K.-i. Watanabe, K. E. Smith, N. Hara and F. Enescu, have used the…

Let $R$ be a commutative ring with unity, $M$ be a unitary $R$-module and $G$ a finite abelian group (viewed as a $\mathbb{Z}$-module). The main objective of this paper is to study properties of mod-annihilators of $M$. For $x \in M$, we…

We study the tensor category $\cQ$ of tilting modules over a quantum group $U_q$ with divided powers. The set $X_+$ of dominant weights is a union of closed alcoves $\oC_w$ numbered by the elements $w\in W^f$ of a certain subset of affine…

In this article we investigate the fibers of relative $D$-modules. In general we prove that there exists an open, Zariski dense subset of the vanishing set of the annihilator over which the fibers of a cyclic relative $D$-module are…