Irreducible tensor product modules over the W-algebra W(2,2)

We introduce the notion of a ring with the condition of constructivizable modules in some class and study the simplest properties of such rings. We find a sufficient test for constructivizibility of the tensor product of modules. We also prove that there exist such modules whose tensor product over the ring of integers is not constructivizable.

Tensor product of highest weight modules and intermediate modules for Virasoro algebra have been studied around 1997. Since then the irreducibility problem for tensor product of modules is open. We consider the loop-Virasoro algebra [Formula: see text], where Vir is the Virasoro algebra and [Formula: see text] is a commutative associative unital algebra over [Formula: see text]. In this paper, we study the irreducibility problem for the tensor product of highest weight modules and intermediate modules for [Formula: see text]. Finally we found out a necessary and sufficient condition for such modules to be isomorphic.

In this paper, we have the principal goal is to study a topography property of important algebraic construction namely the quotient module. We use a new tool with a quotient module which is a tensor product of modules. Therefore all topography submodules in this notion are a tensor product. The meaning of the tensor module introduced in this notion and the important fact of this article is to explain the quotient module when all submodules are tensor. Finally, several results have been obtained about the direct sum of the finite quotient module.

We explore questions of projectivity and tensor products of modules for finite dimensional Hopf algebras. We construct many classes of examples in which tensor powers of nonprojective modules are projective and tensor products of modules in one order are projective but in the other order are not. Our examples are smash coproducts with duals of group algebras, some having algebra and coalgebra structures twisted by cocycles. We apply support variety theory for these Hopf algebras as a tool in our investigations.

We show that the Gelfand–Kirillov dimension for modules over quantum Laurent polynomials is additive with respect to tensor products over the base field. We determine the Brookes–Groves invariant associated with a tensor product of modules. We study strongly holonomic modules and show that there are nonholonomic simple modules.

The Loewy length of a tensor product of modules of a dihedral two-group

Given a Hopf algebra H and an algebra A that is an H-module algebra we consider the category of left H-modules and A-bimodules [Formula: see text], where morphisms are just right A-linear maps (not necessarily H-equivariant). Given a twist [Formula: see text] of H we then quantize (deform) H to [Formula: see text], A to A⋆ and correspondingly the category [Formula: see text] to [Formula: see text]. If we consider a quasitriangular Hopf algebra H, a quasi-commutative algebra A and quasi-commutative A-bimodules, we can further construct and study tensor products over A of modules and of morphisms, and their twist quantization. This study leads to the definition of arbitrary (i.e., not necessarily H-equivariant) connections on quasi-commutative A-bimodules, to extend these connections to tensor product modules and to quantize them to A⋆-bimodule connections. Their curvatures and those on tensor product modules are also determined.

Module tensor product of subnormal modules need not be subnormal

This paper establishes several results for coalgebraic structure in -categories, specifically with connections to the spectral noncommutative geometry of cobordism theories.We prove that the categories of comodules and modules over a bialgebra always admit suitably structured monoidal structures in which the tensor product is taken in the ambient category (as opposed to a relative (co)tensor product over the underlying algebra or coalgebra of the bialgebra).We give two examples of higher coalgebraic structure: first, following Hess we show that for a map of E n -ring spectra : A B, the associated -category of descent data is equivalent to the -category of comodules over B A B, the so-called descent coring; secondly, we show that Thom spectra are canonically equipped with a highly structured comodule structure which is equivalent to the -categorical Thom diagonal of Ando, Blumberg, Gepner, Hopkins and Rezk (which we describe explicitly) and that this highly structured diagonal decomposes the Thom isomorphism for an oriented Thom spectrum in the expected way indicating that Thom spectra are good examples of spectral noncommutative torsors.

In this paper, using generating functions, we study two categories Open image in new window and Open image in new window of modules for twisted affine Lie algebras Open image in new window , which were firstly introduced and studied for untwisted affine Lie algebras by H. -S. Li [Math Z, 2004, 248: 635–664]. We classify integrable irreducible Open image in new window -modules in categories Open image in new window and Open image in new window , where Open image in new window is proved to contain the well-known evaluation modules and Open image in new window to unify highest weight modules, evaluation modules and their tensor product modules. We determine also the isomorphism classes of those irreducible modules.

The present chapter is devoted to the study of Noetherian rings, Projective modules, Injective Modules, Tensor product of modules, Grothendieck, and Whitehead groups of rings.

This series aims to report new developments in mathematical research and teaching -quickly, informally and at a high level.The type of material considered for publication includes: 1.Preliminary drafts of original papers and monographs 2. Lectures on a new field, or presenting a new angle on a classical field 3. Seminar work-outs 4. Reports of meetings, provided they are a) of exceptional interest or b) devoted to a single topic.

The Knizhnik-Zamolodchikov equation associated with $s\ell_2$ is considered. The transition functions between asymptotic solutions to the Knizhnik-Zamolodchikov equation are described. A connection between asymptotic solutions and the crystal base in the tensor product of modules over the quantum group $U_qs\ell_2$ is established, in particular, a correspondence between the Bethe vectors of the Gaudin model of an inhomogenious magnetic chain and the $\Bbb Q-$basis of the crystal base.

ТЕНЗОРНОЕ ПРОИЗВЕДЕНИЕ МОДУЛЕЙ НАД CSP-КОЛЬЦАМИ

In the present paper, non-weight modules over the super-BMS3 algebras [Formula: see text] ([Formula: see text] or [Formula: see text]) are constructed. Assume that [Formula: see text] and [Formula: see text] are the Cartan subalgebra (modulo center) of [Formula: see text] and [Formula: see text], respectively. These modules over [Formula: see text] when restricted to the [Formula: see text] are free of rank [Formula: see text], while these modules over [Formula: see text] when restricted to the [Formula: see text] are free of rank [Formula: see text]. Then we determine the necessary and sufficient conditions for these modules being simple, as well as determining the necessary and sufficient conditions for two [Formula: see text]-modules being isomorphic.