Related papers: Quotients of Standard Hilbert Modules

The parallel sum for adjoinable operators on Hilbert $C^*$-modules is introduced and studied. Some results known for matrices and bounded linear operators on Hilbert spaces are generalized to the case of adjointable operators on Hilbert…

In this paper we present a procedure for computing the rational sum of the Hilbert series of a finitely generated monomial right module $N$ over the free associative algebra $K\langle x_1,\ldots,x_n \rangle$. We show that such procedure…

The modularity of an elliptic curve $E/\mathbb Q$ can be expressed either as an analytic statement that the $L$-function is the Mellin transform of a modular form, or as a geometric statement that $E$ is a quotient of a modular curve…

Non-commutative Hilbert schemes, introduced by M. V. Nori, parametrize left ideals of finite codimension in free algebras. More generally, parameter spaces of finite codimensional submodules of free modules over free algebras are…

We deal with the reduction theory of a $W^*$-algebra $M$ along a $W^*$-subalgebra $Z$ of the centre of $M$. This is done by using Hilbert modules naturally constructed by suitable spatial representations of the abelian $W^*$-algebra $Z$. We…

This paper is a continuation to understand Heisenberg vertex algebras in terms of moduli spaces of their conformal structures. We study the moduli space of the conformal structures on a Heisenberg vertex algebra that have the standard fixed…

In this paper we give some evidence for the Tate (and Hodge) conjecture(s) for a class of Hilbert modular fourfolds X, whose connected components arise as arithmetic quotients of the fourfold product of the upper half plane by congruence…

Consider a bounded symmetric domain $\Omega$ with a finite pseudo-reflection group acting on it as a subgroup of the group of automorphisms. This gives rise to quotient domains by means of basic polynomials $\theta$ which by virtue of being…

In a recent paper by Harada, Seceleanu, and \c{S}ega, the Hilbert function, betti table, and graded minimal free resolution of a general principal symmetric ideal are determined when the number of variables in the polynomial ring is…

Let $M$ be a finitely generated module of dimension $d$ and depth $t$ over a Noetherian local ring ($A, {\mathfrak m}$) and $I$ an ${\mathfrak m}$-primary ideal. In the main result it is shown that the last $t$ Hilbert coefficients…

Abstract. Let G be a complex reductive group and A be an Abelian variety of dimension d over $\mathbb{C}$. We determine the Poincar\'e polynomials and also the mixed Hodge polynomials of the moduli space $\mathcal{M}_{A}^{H}(G)$ of G-Higgs…

The aim of this paper is to build a theory of commutative and noncommutative {\it injective} valuations of various algebras (including algebras with zero divisors). The targets of our valuations are (well-)ordered commutative and…

The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…

The codomain category of a generalized homology theory is the category of modules over a ring. For an abelian category A, an A-valued (generalized) homology theory is defined by formally replacing the category of modules with the category…

We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…

Let $L$ be a finite dimensional Lie algebra over a field of characteristic $0$. Then by the original Levi theorem, $L = B \oplus R$ where $R$ is the solvable radical and $B$ is some maximal semisimple subalgebra. We prove that if $L$ is an…

Guo and the second author have shown that the closure $[I]$ in the Drury-Arveson space of a homogeneous principal ideal $I$ in $\mathbb{C}[z_1,...,z_n]$ is essentially normal. In this note, the authors extend this result to the closure of…

We study closures of GL_2(R)-orbits on the total space of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum,…

Considering the deeper reasons of the appearance of a remarkable counterexample by J.~Kaad and M.~Skeide [17] we consider situations in which two Hilbert C*-modules $M \subset N$ with $M^\bot = \{ 0 \}$ over a fixed C*-algebra $A$ of…

We introduce and study some new uniform structures for Hilbert $C^*$-modules over an algebra $A$. In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of…