We introduce a notion of strongly C×-graded generalized g-twisted V -module for an automorphism g, not necessarily of finite order, of a vertex operator algebra. Let V = ∐ n∈Z V(n) be a vertex operator algebra such that V(0) = C1 and V(n) = 0 for n < 0 and let u be an element of V of weight 1 such that L(1)u = 0, ResxY (u, x) has only real eigenvalues, and the sizes of the Jordan blocks of Resx...

Recently the understanding of the cohomology of the Hilbert scheme of points on K3 surfaces has been greatly improved by Lehn and Sorger [18]. Their approach uses the connection of the Hilbert scheme to the orbifolds given by the symmetric products of these surfaces. We introduced a general theory replacing cohomology algebras or more generally Frobenius algebras in a setting of global quotient...

Let R be a commutative ring with identity. Let N and K be two submodules of a multiplication R-module M. Then N=IM and K=JM for some ideals I and J of R. The product of N and K denoted by NK is defined by NK=IJM. In this paper we characterize some particular cases of multiplication modules by using the product of submodules.

Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free parameter and is generated by differential-difference (“Dunkl”) operators, multiplication by coordinate functions and the group algebra. By specializing Griffeth’s (arχiv:0707.0251) results for the ...

The first Weyl algebra over k, A1 = k〈x, y〉/(xy− yx− 1) admits a natural Z-grading by letting deg x = 1 and deg y = −1. Paul Smith showed that gr -A1 is equivalent to the category of quasicoherent sheaves on a certain quotient stack. Using autoequivalences of gr -A1, Smith constructed a commutative ring C, graded by finite subsets of the integers. He then showed gr -A1 ≡ gr -(C,Zfin). In this p...

Let S be a polynomial ring in n variables over a field K of characteristic 0. A numerical characterization of all possible extremal Betti numbers of any graded submodule of a finitely generated graded free S-module is given. 2010 Mathematics Subject Classification: 13B25, 13D02, 16W50.

The purpose of this paper is to initiate a new attack on Arveson’s resistant conjecture, that all graded submodules of the d-shift Hilbert module H are essentially normal. We introduce the stable division property for modules (and ideals): a normed module M over the ring of polynomials in d variables has the stable division property if it has a generating set {f1, . . . , fk} such that every h ...

Let A be a (G,χ)-Hopf algebra with bijective antipode and let M be a G-graded A-bimodule. We prove that there exists an isomorphism HH∗gr(A,M)∼= Ext∗A-gr ( K,ad (M) ) , where K is viewed as the trivial graded A-module via the counit of A, adM is the adjoint A-module associated to the graded A-bimodule M and HH∗gr denotes the G-graded Hochschild cohomology. As an application, we deduce that the ...

A notion of curvature is introduced in multivariable operator theory. The curvature invariant of a Hilbert module over C[z(1),., z(d)] is a nonnegative real number which has significant extremal properties, which tends to be an integer, and which is hard to compute directly. It is shown that for graded Hilbert modules, the curvature agrees with the Euler characteristic of a certain finitely gen...

Let $G$ be a group with identity $e$. $R$ $G$-graded commutative ring and $M$ graded $R$-module. In this paper, we introduce the concept of classical strongly 2-absorbing second submodules modules over rings. A number results concerning these classes their homogeneous components are given.