We introduce a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type associated with $\mathbb{Z}_k$-code for $k \ge 2$. Our argument is based on the $\mathbb{Z}_k$-symmetry among simple current modules parafermion $K(\mathfrak{sl}_2, k)$. show that it naturally realized as commutant certain subalgebra in lattice algebra. Furthermore, we construct all irreducible in...

This paper is an effort to continue the legacy of classically successful theory Toeplitz operators on Hardy space over unit disk a new domain in $${\mathbb {C}}^d$$ —the symmetrized polydisk. We obtain algebraic characterizations operators, analytic compact perturbation and dual operators. then revisit operator this considered first Biswas Shyam Roy (J Funct Anal 266:6224–6255, 2014), study gen...

A functional model for nondissipative unbounded perturbations of an unbounded self-adjoint operator on a Hilbert space X is constructed. This model is analogous to the Nagy– Foias model of dissipative operators, but it is linearly similar and not unitarily equivalent to the operator. It is attached to a domain of parabolic type, instead of a half-plane. The transformation map from X to the mode...

We consider in general terms dynamical systems with finite-dimensional, nonsimply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that arise from the non-simply connectedness of the classical configuration space. We define the quantum theory on the universal cover but restrict the algebra of...

We introduce the notion of fibred action of a group bundle on a C0(X)algebra. By using such a notion, a characterization in terms of induced C*-bundles is given for C*-dynamical systems such that the relative commutant of the fixed-point C*-algebra is minimal (i.e., it is generated by the centre of the given C*-algebra and the centre of the fixed-point C*algebra). A class of examples in the set...

Identified are a number of conditions on square patterns that are closely related to allowing commutativity with the full pattern. Implications and examples that show non-implications are given, along with a graph that summarizes the provided information. A complete description of commutativity with the full pattern is given in both the irreducible case and the reducible case in which there are...