Related papers: Decomposition of the tensor product of two Hilbert…

Let $(A,\mathfrak{m})$ be a complete intersection ring of dimension $d$ and let $I$ be an $\mathfrak{m}$-primary ideal. Let $M$ be a maximal \CM \ $A$-module. For $i = 0,1,\cdots,d$, let $e_i^I(M)$ denote the $i^{th}$ Hilbert -coefficient…

The Hecke-Kiselman algebra of a finite oriented graph $\Theta$ over a field $K$ is studied. If $\Theta$ is an oriented cycle, it is shown that the algebra is semiprime and its central localization is a finite direct product of matrix…

The $\star_M$-family of tensor-tensor products is a framework which generalizes many properties from linear algebra to third order tensors. Here, we investigate positive semidefiniteness and semidefinite programming under the…

In the context of finite tensor products of Hilbert spaces, we prove that similarity of a tensor product of operator semigroups to a contraction semigroup is equivalent to the corresponding similarity for each factor, after an appropriate…

Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative analogues of tensor bundles. For…

In this semi-expository paper, we first explain key notions from current quantum information theory and criteria for them in a coherent way. These include separability/entanglement, Schmidt numbers of bi-partite states and block-positivity,…

We study that natural inclusions $C^b(X) \tensor A$ into $C^b(X,A)$ and $C^b(X, C^b(Y))$ into $C^b(X \times Y)$. In particular, excepting trivial cases, both these maps are isomorphisms only when $X$ and $Y$ are pseudocompact. This implies…

Let $R$ be a commutative Noetherian local ring. We study tensor products involving a finitely generated $R$-module $M$ through the natural action of its endomorphism ring. In particular, we study torsion properties of self tensor products…

We characterize the (essentially) decreasing sequences of positive numbers $\beta$ = ($\beta$ n) for which all composition operators on H 2 ($\beta$) are bounded, where H 2 ($\beta$) is the space of analytic functions f in the unit disk…

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations. Then we study their behaviour under the…

An operator system modulo the kernel of a completely positive linear map of the operator system gives rise to an operator system quotient. In this paper, operator system quotients and quotient maps of certain matrix algebras are considered.…

We consider Hilbert's tenth problem for two families of noncommutative rings. Let $K$ be a field of characteristic $p$. We start by showing that Hilbert's tenth problem has a negative answer over the twisted polynomial ring $K\{\tau\}$ and…

For a semibounded sesquilinear form ${\mathfrak t}$ in a Hilbert space ${\mathfrak H}$ there exists a representing map $Q$ from ${\mathfrak H}$ to another Hilbert space ${\mathfrak K}$, such that ${\mathfrak t}[\varphi, \psi]-c(\varphi,…

We give a complete classification of reductive symmetric pairs (g, h) with the following property: there exists at least one infinite-dimensional irreducible (g,K)-module X that is discretely decomposable as an (h,H \cap K)-module. We…

We prove that, analogous to the HK density function, (used for studying the Hilbert-Kunz multiplicity, the leading coefficient of the HK function), there exists a $\beta$-density function $g_{R, {\bf m}}:[0,\infty)\longrightarrow {\mathbb…

In this note we present a complete computation of the topological K-theory of the reduced C*-algebra of a semidirect product of the form $\Gamma=\mathbb{Z}^n\rtimes_\rho\mathbb{Z}/2$ with no further assumptions about of the conjugacy action…

Let $k[X] = k[x_{i,j}: i = 1,..., m; j = 1,..., n]$ be the polynomial ring in $m n$ variables $x_{i,j}$ over a field $k$ of arbitrary characteristic. Denote by $I_2(X)$ the ideal generated by the $2 \times 2$ minors of the generic $m \times…

Let $\Gamma$ be a torsion-free arithmetic group acting on its associated global symmetric space $X$. Assume that $X$ is of non-compact type and let $\Gamma$ act on the geodesic boundary $\partial X$ of $X$. Via general constructions in…

We provide a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace K inside the second exterior product of a vector space, as well as a sharp upper bound for its Hilbert function.…

We present an explicit product formula for the spherical functions of the compact Gelfand pairs $(G,K_1)= (SU(p+q), SU(p)\times SU(q))$ with $p\ge 2q$, which can be considered as the elementary spherical functions of one-dimensional…