Related papers: A new duality via the Haagerup tensor product

Let $\mathbb{S}$ denote the oscillatory module over the complex symplectic Lie algebra $\mathfrak{g}= \mathfrak{sp}(\mathbb{V}^{\mathbb{C}},\omega).$ Consider the $\mathfrak{g}$-module…

We consider compact group actions on C*- and W*- algebras. We prove results that relate the duality property of the action (as defined in the Introduction) with other relevant properties of the system such as the relative commutant of the…

We propose a number of new Seiberg dualities of N=1 quiver gauge theories. The new Seiberg dualities originate in new S-dualities of N=2 superconformal field theories recently proposed by Gaiotto. N=2 S-dual theories deformed by suitable…

We introduce quotient maps in the category of operator systems and show that the maximal tensor product is projective with respect to them. Whereas, the maximal tensor product is not injective, which makes the $({\rm el},\max)-nuclearity…

Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\tau_i:X \to X$ for $1 \le i \le n$. To this we associate two topological conjugacy algebras which emerge as the natural candidates for the universal algebra…

We generalize our picture in [arXiv:0904.1744], and consider a pure abelian gauge theory on a four-manifold with nonlocal operators of every codimension arbitrarily and simultaneously inserted. We explicitly show that (i) the theory enjoys…

We affirmatively resolve a question posed by Uffe Haagerup in 1975 on the positive version of the bipolar theorem on the dual spaces of C$^*$-algebras. As a direct consequence, we obtain a complete set of four positive Hahn-Banach…

Continuous actions of topological groups on compact Hausdorff spaces $X$ are investigated which induce almost periodic functions in the corresponding commutative C*-algebra. The unique invariant mean on the group resulting from averaging…

We study tensor structures on (Rep G)-module categories defined by actions of a compact quantum group G on unital C*-algebras. We show that having a tensor product which defines the module structure is equivalent to enriching the action of…

Using the natural duality between linear functionals on tensor products of C*-algebras with the trace class operators on a Hilbert space H and linear maps of the C*-algebra into B(H), we give two characterizations of separability, one…

Let $\lambda: \tilde{G}\to G$ be the non-trivial double covering of the symplectic group $G=Sp(V,\omega)$ of the symplectic vector space $(V,\omega)$ by the metaplectic group $\tilde{G}=Mp(V,\omega).$ In this case, $\lambda$ is also a…

We propose new vertex operators, both the type I and the type II dual, of the elliptic quantum toroidal algebra U_{t_1,t_2,p}(gl_{1,tor}) by combining representations of U_{t_1,t_2,p}(gl_{1,tor}) and the notions of the elliptic stable…

Let $p\in(1,\infty)$. We show that there is an isomorphism from any separable unital subalgebra of $B(\ell^{2})/K(\ell^{2})$ onto a subalgebra of $B(\ell^{p})/K(\ell^{p})$ that preserves the Fredholm index. As a consequence, every separable…

We introduce and investigate using Hilbert modules the properties of the Fourier algebra A(G) for a locally compact groupoid G. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a…

In this paper we show that every conjugation $C$ on the Hardy-Hilbert space $H^{2}$ is of type $C=T^{*}C_{1}T$, where $T$ is an unitary operator and $C_{1}f\left(z\right)=\overline{f\left(\overline{z}\right)}$, with $f\in H^{2}$. In the…

Summarizing basic facts from abstract topological modules over Colombeau generalized complex numbers we discuss duality of Colombeau algebras. In particular, we focus on generalized delta functionals and operator kernels as elements of dual…

Let R be an integral domain, let a non-zero h in R be such that k := R/hR is a field, and let HA be the category of torsionless (or flat) Hopf algebras over R. We call H in HA a "quantized function algebra" (=QFA), resp. "quantized…

In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary commutative rings in such a way that they can…

Let $\mathcal{G}$ be a locally compact \'{e}tale groupoid and $\mathscr{L}(L^2(\mathcal{G}))$ be the $C^*$-algebra of adjointable operators on the Hilbert $C^*$-module $L^2(\mathcal{G})$. In this paper, we discover a notion called…

Noncommutative K\"ahler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we introduce the notion of a \emph{compact quantum homogeneous…