Related papers: A Fej\'{e}r theorem for boundary quotients arising…

This paper extends the decorated Teichm\"uller theory developed before for punctured surfaces to the setting of ``bordered'' surfaces, i.e., surfaces with boundary, and there is non-trivial new structure discovered. The main new result…

In this article, we prove $K$-stability for a family of $C^*$-algebras, which are generated by a finite set of unitaries and isometries satisfying twisted commutation relations. This family includes the $C^*$-algebra of doubly non-commuting…

We consider GL$_m$-dimers of triangulations of regular convex $n$-gons, which give rise to a dimer model with boundary $Q$ and a dimer algebra $\Lambda_Q$. Let $e_b$ be the sum of the idempotents of all the boundary vertices, and…

In this article we show that the main C*-algebras describing the canonical commutation relations of quantum physics, i.e., the Weyl and resolvent algebras, are in the class of F{\o}lner C*-algebras, a class of C*-algebras admitting a kind…

We associate to each discrete partial dynamical system a universal C*-algebra generated by partial isometries satisfying relations given by a Boolean algebra connected to the discrete partial dynamical system in question. We show that for…

Let $\Delta$ be an infinite, locally finite tree with more than two ends. Let $\Gamma<\aut(\Delta)$ be an acylindrical uniform lattice. Then the boundary algebra $\cl A_\Gamma = C(\partial\Delta)\rtimes \Gamma$ is a simple Cuntz-Krieger…

We present an analytical approach to construct the Lie algebra of finite-dimensional subsystems of the driven asymmetric top rotor. Each rotational level is degenerate due to the isotropy of space, and the degeneracy increases with…

We study properties of the category of modules of an algebra object A in a tensor category C. We show that the module category inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As…

In this memoir we develop a framework to study rigidity problems for Roe-like C*-algebras of countably generated coarse spaces. The main goal is to give a complete and self-contained solution to the problem of C*-rigidity for proper…

Under a minimum of assumptions, we develop in generality the basic theory of universal algebra in a symmetric monoidal closed category $\mathcal{V}$ with respect to a specified system of arities $j:\mathcal{J} \hookrightarrow \mathcal{V}$.…

A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The C*-algebra generated by the partial isometries is thus a quotient of…

In this paper, we prove a Morse index theorem for the index form of regular Lagrangian system with selfadjoint boundary condition.

Fej\'er's theorem guarantees norm convergence of Ces\`aro means of Taylor partial sums in the Hardy space, whereas such convergence generally fails in weighted Dirichlet-type spaces, especially in the higher-order setting. In this paper, we…

We prove a Noether-Deuring theorem for the derived category of bounded complexes of modules over a Noetherian algebra.

Let $f: D \rightarrow \Omega$ be a complex analytic function. The Julia quotient is given by the ratio between the distance of $f(z)$ to the boundary of $\Omega$ and the distance of $z$ to the boundary of $D.$ A classical…

We construct C*-dynamical systems for the dynamics of classical infinite particle systems describing harmonic oscillators interacting with arbitrarily many neighbors on lattices, as well on more general structures. Our approach allows…

We show that if a flat group scheme acts properly, with finite stabilizers, on an algebraic space, then a quotient exists as a separated algebraic space. More generally we show any flat groupid for which the family of stabilizers is finite…

Let $P$ be a unital subsemigroup of a group $G$. We propose an approach to $\mathrm{C}^*$-algebras associated to product systems over $P$. We call the $\mathrm{C}^*$-algebra of a given product system $\mathcal{E}$ its covariance algebra and…

We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time dependence of a matrix element of fermionic systems related to the {\it Orthogonality…

We introduce the Haagerup property for twisted groupoid $C^*$-dynamical systems in terms of naturally defined positive-definite operator-valued multipliers. By developing a version of `the Haagerup trick' we prove that this property is…