The category of graded, bicommutative Hopf algebras over the prime eld with p elements is an abelian category which is equivalent, by work of Schoeller, to a category of graded modules, known as Dieudonn e modules. Graded ring objects in Hopf algebras are called Hopf rings, and they arise in the study of unstable cohomology operations for extraordinary cohomology theories. The central point of ...

In this paper we define and study a family of Z+–graded modules for the polynomial valued current algebra g[t] and the twisted current algebra g[t] associated to a finite–dimensional classical simple Lie algebra g and a non–trivial diagram automorphism of g. The modules which we denote as KR(mωi) and KR (mωi) respectively are indexed by pairs (i,m), where i is a node of the Dynkin diagram and m...

In this paper we define and study a family of Z+–graded modules for the polynomial valued current algebra g[t] and the twisted current algebra g[t] associated to a finite–dimensional classical simple Lie algebra g and a non–trivial diagram automorphism of g. The modules which we denote as KR(mωi) and KR (mωi) respectively are indexed by pairs (i,m), where i is a node of the Dynkin diagram and m...

We study a variety for graded maximal Cohen–Macaulay modules, which was introduced by Dao and Shipman. The main result of this paper asserts that there are only finite number isomorphism classes modules with fixed Hilbert series over algebras countable representation type.

In this paper, we study a class of Zd-graded modules, which are constructed using Shen–Larsson’s functor from sld-modules V, for the Lie algebras divergence zero vector fields on tori and quantum tori. We determine irreducibility these modules finite-dimensional or infinite-dimensional V unified method. particular, provide new irreducible weight with spaces corresponding algebras.

Abstract. We study h-vectors and graded Betti numbers of level modules up to multiplication by a rational number. Assuming a conjecture on the possible graded Betti numbers of Cohen-Macaulaymodules we get a description of the possible h-vectors of level modules up to multiplication by a rational number. We also determine, again up to multiplication by a rational number, the cancellable h-vector...