Related papers: Ergodic theory for quantum semigroups

Calder\'on-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we introduce a new approach for general measure spaces which admit a Markov…

Using Hernandez-Leclerc's isomorphism between the derived Hall algebra of a representation-finite quiver $Q$ and the quantum Grothendieck ring of the quantum loop algebra of the Dynkin type of $Q$, we lift the (quantum) cluster algebra…

This note is an attempt to extend "Geometric Langlands Conjecture" from algebraic curves to algebraic surfaces. We introduce certain Hecke-type operators on vector bundles on an algebraic surface. The crucial observation is that the algebra…

In this paper, we study the ergodic theorem for infinite-dimensional quantum Markov semigroups, originally introduced by Frigerio and Verri in 1982, and its latest version developed by Carbone and Girotti in 2021. We provide a sufficient…

The algebras of the symmetry operators for the Hamilton-Jacobi and Klein-Gordon-Fock equations are found for a charged test particle moving in an external electromagnetic field in a spacetime manifold, on the isotropic (null) hypersurface…

In this paper we obtain some noncommutative multiplier theorems and maximal inequalities on semigroups. As applications, we obtain the corresponding individual ergodic theorems. Our main results extend some classical results of Stein and…

This paper is devoted to the study of noncommutative ergodic theorems for connected amenable locally compact groups. For a dynamical system $(\mathcal{M},\tau,G,\sigma)$, where $(\mathcal{M},\tau)$ is a von Neumann algebra with a normal…

The paper proposes a construction of a quantum differentiation operator defined on the spaces of complex-valued functions of $p$-adic argument, and taking values in the algebra of bounded operators on a Hilbert space. The properties of this…

The given study uses the methods to identify compactifications of semigroups $S\subset L(X),$ which reside in the space $L(X).$ This method generalizes in some sense the deLeeuw-Glicksberg-Theory to a greater class of functions. The…

We prove a decomposition theorem for the equivariant K-theory of actions of affine group schemes G of finite type over a field on regular separated noetherian algebraic spaces, under the hypothesis that the actions have finite geometric…

Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad for semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial…

Let $S$ be a subsemigroup of a second countable locally compact group $G$, such that $S^{-1}S=G$. We consider the $C^*$-algebra $C^*_\delta(S)$ generated by the operators of translation by all elements of $S$ in $L^2(S)$. We show that this…

This expository article presents a unified ring theoretic approach, based on the theory of Frobenius algebras, to a variety of results on Hopf algebras. These include a theorem of S. Zhu on the degrees of irreducible representations, the…

Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…

Power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in von Neumann's ergodic theorem with continuous time is considered. All possible exponents of the considered power-law convergence are found; for…

We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in $\mathbb{C}^{\mathbf{n}}$. For the algebras of elliptic type we find a new representation, namely as the algebra of operators which…

We give the construction of a class of weak Hopf algebras (or quantum groupoids) associated to a matched pair of groupoids and certain cocycle data. This generalizes a now well-known construction for Hopf algebras, first studied by G. I.…

A connection between the Galois-theoretic approach to semi-abelian homology and the homological closure operators is established. In particular, a generalised Hopf formula for homology is obtained, allowing the choice of a new kind of…

Let $\Gamma=\Gamma(N)$ be a principal congruence subgroup of $SL_2(\mathbb Z)$. In this paper, we extend the theory of modular Hecke algebras due to Connes and Moscovici to define the algebra $\mathcal Q(\Gamma)$ of quasimodular Hecke…

A major topic of (classical) ergodic theory is to examine qualitatively how the phase space of dynamical systems is penetrated by the orbits of their dynamics. We consider interacting qubit systems with dynamics according to 4-local…