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It has been asked whether there is a version of the tensor product property for support varieties over finite dimensional algebras defined in terms of Hochschild cohomology. We show that in general no such version can exist. In particular,…
We study moduli spaces of (semi-)stable representations of one-point extensions of quivers by rigid representations. This class of moduli spaces unifies Grassmannians of subrepresentations of rigid representations and moduli spaces of…
We discuss the obstruction to the construction of a multiparticle field theory on a $\kappa$-Minkowski noncommutative spacetime: the existence of multilocal functions which respect the deformed symmetries of the problem. This construction…
We give a complete characterization of invariant subspaces for $(M_{z_1}, \ldots, M_{z_n})$ on the Hardy space $H^2(\mathbb{D}^n)$ over the unit polydisc $\mathbb{D}^n$ in $\mathbb{C}^n$, $n >1$. In particular, this yields a complete set of…
In this paper we study modular tensor categories (braided rigid balanced tensor categories with additional finiteness and non-degeneracy conditions), in particular, representations of quantum groups at roots of unity. We show that the…
Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker…
The modular data of a modular category $\mathcal{C}$, consisting of the $S$-matrix and the $T$-matrix, is known to be an incomplete invariant of $\mathcal{C}$. More generally, the invariants of framed links and knots defined by a modular…
We extend the de Branges-Beurling theorem characterizing the shift-invariant spaces boundedly contained in the Hardy space of square-summable power series to the full Fock space over $\mathbb{C} ^d$. Here, the full Fock space is identified…
Noncommutative domain algebras are noncommutative analogues of the algebras of holomorphic functions on domains of $\C^n$ defined by holomorphic polynomials, and they generalize the noncommutative Hardy algebras. We present here a complete…
We use operator algebras and operator theory to obtain new result concerning Berezin quantization of compact K\"ahler manifolds. Our main tool is the notion of subproduct systems of finite-dimensional Hilbert spaces, which enables all…
We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…
The goal of this paper is to study the structure of noncommutative weighted shifts, their properties, and to understand their role as models (up to similarity) for $n$-tuples of operators on Hilbert spaces as well as their implications to…
The present paper is an extension of a previous paper written in collaboration with Markus Reineke dealing with quiver representations. The aim of the paper is to generalize the theory and to provide a comprehensive theory of…
In the Drury-Arveson space, we consider the subspace of functions whose Taylor coefficients are supported in the complement of a set $Y\subset\mathbb{N}^d$ with the property that $Y+e_j\subset Y$ for all $j=1,\dots,d$. This is an easy…
Let B(H) be the algebra of all bounded linear operators on a Hilbert space H. The main goal of the paper is to find large classes of noncommutative domains in B(H) with prescribed universal operator models, acting on the full Fock space…
In this paper we solve several problems concerning joint similarity to n-tuples of operators in noncommutative varieties in $[B(\cH)^n]_1$ associated with positive regular free holomorphic functions in $n$ noncommuting variables and with…
The Fock space can be characterized (up to a positive multiplicative factor) as the only Hilbert space of entire functions in which the adjoint of derivation is multiplication by the complex variable. Similarly (and still up to a positive…
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…
We initiate the study of a class of noncommutative domains of n-tuples of bounded linear operators on a Hilbert space, which is generated by certain positivity conditions on polynomials in n noncommutative indeterminates. We obtain Fatou…
We study the invariant subspaces generated by inner functions for a class of $\mathcal{P}^t(\mu)$-spaces which can be identified as spaces of analytic functions in the unit disk $\mathbb{D}$, where $\mu$ is a measure supported in the closed…