The structure of the inverse system of Gorenstein k-algebras

Macaulay's Inverse System gives an effective method to construct Artinian Gorenstein k-algebras. To date a general structure for Gorenstein k-algebras of any dimension (and codimension) is not understood. In this paper we extend Macaulay's correspondence characterizing the submodules of the divided power ring in one-to-one correspondence with Gorenstein d-dimensional k-algebras. We discuss effective methods for constructing Gorenstein graded rings. Several examples illustrating our results are given.Comment: 19 pages, to appear in Advances in Mathematic

Transmutations between Singular and Subsingular Vectors of the N=2 Superconformal Algebras

We present subsingular vectors of the N=2 superconformal algebras other than the ones which become singular in chiral Verma modules, reported recently by Gato-Rivera and Rosado. We show that two large classes of singular vectors of the Topological algebra become subsingular vectors of the Antiperiodic NS algebra under the topological untwistings. These classes consist of BRST- invariant singular vectors with relative charges $q=-2,-1$ and zero conformal weight, and no-label singular vectors with $q=0,-1$. In turn the resulting NS subsingular vectors are transformed by the spectral flows into subsingular and singular vectors of the Periodic R algebra. We write down these singular and subsingular vectors starting from the topological singular vectors at levels 1 and 2.Comment: 21 pages, Latex. Minor improvements. Very similar to the version published in Nucl. Phys.

Associative-algebraic approach to logarithmic conformal field theories

We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non--semi-simple associative algebras appearing in their lattice regularizations (as discussed in a companion paper). Here we work out in detail two examples of theories derived as the continuum limit of XXZ spin-1/2 chains, which are related to spin chains with supersymmetry algebras gl($n|n$) and gl($n+1|n$), respectively, with open (or free) boundary conditions in all cases. These theories can also be viewed as vertex models, or as loop models. Their continuum limits are boundary conformal field theories (CFTs) with central charge $c=-2$ and $c=0$ respectively, and in the loop interpretation they describe dense polymers and the boundaries of critical percolation clusters, respectively. We also discuss the case of dilute (critical) polymers as another boundary CFT with $c=0$. Within the supersymmetric formulations, these boundary CFTs describe the fixed points of certain nonlinear sigma models that have a supercoset space as the target manifold, and of Landau-Ginzburg field theories. The submodule structures of indecomposable representations of the Virasoro algebra appearing in the boundary CFT, representing local fields, are derived from the lattice. A central result is the derivation of the fusion rules for these fields

A formal language for the specification and verification of synchronous and asynchronous circuits

A formal hardware description language for the intended application of verifiable asynchronous communication is described. The language is developed within the logical framework of the Nqthm system of Boyer and Moore and is based on the event-driven behavioral model of VHDL, including the basic VHDL signal propagation mechanisms, the notion of simulation deltas, and the VHDL simulation cycle. A core subset of the language corresponds closely with a subset of VHDL and is adequate for the realistic gate-level modeling of both combinational and sequential circuits. Various extensions to this subset provide means for convenient expression of behavioral circuit specifications

Homology of artinian and Matlis reflexive modules, I

Let R be a commutative local noetherian ring, and let L and L' be R-modules. We investigate the properties of the functors Tor_i^R(L,-) and Ext^i_R(L,-). For instance, we show the following: (a) if L is artinian and L' is noetherian, then Hom_R(L,L') has finite length; (b) if L and L' are artinian, then the tensor product L \otimes_R L' has finite length; (c) if L and L' are artinian, then Tor_i^R(L,L') is artinian, and Ext^i_R(L,L') is noetherian over the completion \hat R; and (d) if L is artinian and L' is Matlis reflexive, then Ext^i_R(L,L'), Ext^i_R(L',L), and Tor_i^R(L,L') are Matlis reflexive. Also, we study the vanishing behavior of these functors, and we include computations demonstrating the sharpness of our results.Comment: 24 page