Related papers: Quantum monadic algebras
We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
We first prove that the K-theoretic Hall algebra of a preprojective algebra of affine type is isomorphic to the positive half of a quantum toroidal quantum group. An essential step consists to deform the K-theoretic Hall algebra so that the…
We propose a semantic representation of the standard quantum logic QL within a classical, normal modal logic, and this via a lattice-embedding of orthomodular lattices into Boolean algebras with one modal operator. Thus our classical logic…
We consider deformations of quantum exterior algebras extended by finite groups. Among these deformations are a class of algebras which we call truncated quantum Drinfeld Hecke algebras in view of their relation to classical Drinfeld Hecke…
We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to…
We consider epimorphisms from quantum minimal surface algebras onto involutroy subalgebras of split real simply-laced Kac-Moody algebras and provide examples of affine and finite type. We also provide epimorphisms onto such Kac-Moody…
The aim of this paper is to show that even if the natural algebraic semantic for modal (normal) logic is modal algebra, the more general class of subordination algebras (roughly speaking, the non symmetric contact algebras) is adequate too…
We introduce Hecke algebras associated to discrete quantum groups with commensurated quantum subgroups. We study their modular properties and the associated Hecke operators. In order to investigate their analytic properties we adapt the…
We encapsulate the basic notions of the theory of vertex algebras into the construction of a comonad on an appropriate category of formal distributions. Vertex algebras are recovered as coalgebras over this comonad.
We give a survey on the developments in a certain theory of quantum vertex algebras, including a conceptual construction of quantum vertex algebras and their modules and a connection of double Yangians and Zamolodchikov-Faddeev algebras…
Varchenko's approach to quantum groups, from the theory of arrangements of hyperplanes, can be usefully applied to q-algebras in general, of which quantum groups and quantum (super) Kac-Moody algebras are special cases. New results are…
First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…
Beyond the crucial role they play in the foundations of the theory of overconvergent modular forms, canonical subgroups have found new applications to analytic continuation of overconvergent modular forms. For such applications, it is…
A correlational dialect is introduced within the quantum theory language to give a unified treatment of finite-dimensional informational/operational quantum theories, infinite-dimensional relativistic quantum theories, and quantum gravity.…
We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the…
We characterize completey (give a necessary and suffcient condition using special neat embeddings)for a relation algebra to belong to the amalgamation, strong amalgamation, and superamalgamation base of the class of representable algebras.…
We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P.M. Soltan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we…
Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor ordering choices ensuring in an anomaly free quantum constraint…