Related papers: Quantum Boolean Algebras
We construct a family of right coideal subalgebras of quantum groups, which have the property that all irreducible representations are one-dimensional, and which are maximal with this property. The obvious examples for this are the standard…
Conformal Galilei algebra contains so(1,2) subalgebra which is the conformal algebra in one dimension. In this note we generalize methods previously developed for one-dimensional many-body systems and construct a unitary map relating a…
Self-similar potentials generalize the concept of shape-invariance which was originally introduced to explore exactly-solvable potentials in quantum mechanics. In this article it is shown that previously introduced algebraic approach to the…
Quantum homogeneous vector bundles are introduced by a direct description of their sections in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies inherited from the quantum groups, and their sections…
In this paper, we present a canonical association of quantum vertex algebras and their $\phi$-coordinated modules to Lie algebra $\gl_{\infty}$ and its 1-dimensional central extension. To this end we construct and make use of another…
Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic…
We introduce a q-analogue MW_q for the meromorphic Weyl algebra, and study the normalization problem and the symmetric powers sym^n(MW_q) for such algebra from a combinatorial viewpoint.
The so called quantized algebras of functions on affine Hecke algebras of type A and the corresponding q-Schur algebras are defined and their irreducible unitarizable representations are classified.
We construct an analog of the subalgebra $Ugl(n)\otimes Ugl(m)$ of $Ugl(m+n)$ in the setting of quantum toroidal algebras and study the restrictions of various representations to this subalgebra.
A catalogue of explicit realizations of representations of (super) Lie algebras and quantum algebras in Fock space is presented.
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
We associate quantum vertex algebras and their $\phi$-coordinated quasi modules to certain deformed Heisenberg algebras.
The quantum dimensions of modules for vertex operator algebras are defined and their properties are discussed. The possible values of the quantum dimensions are obtained for rational vertex operator algebras. A criterion for simple currents…
We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…
We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we find an interesting duality for such objects. A definition of a quantum…
We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of 'quantum' type in all but a few exceptional cases.
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
We study various forms of amalgamation for Boolean algebras with operations. We will also have the occasion to weaken the Boolean structure dealing with MV and BL algebras with operators.