We investigate how a C*-algebra could consist of functions on a noncommutative set: a discretization of a C*-algebra A is a ∗-homomorphism A → M that factors through the canonical inclusion C(X) ⊆ `∞(X) when restricted to a commutative C*-subalgebra. Any C*-algebra admits an injective but nonfunctorial discretization, as well as a possibly noninjective functorial discretization, where M is a C*...

We study the canonical quantization of the damped harmonic oscillator by resorting to the realization of the q-deformation of the Wheyl-Heisenberg algebra (q-WH) in terms of finite difference operators. We relate the damped oscillator hamiltonian to the q-WH algebra and to the squeezing generator of coherent states theory. We also show that the q-WH algebra is the natural candidate to study the...

The paper is devoted to the coherence problem for algebraic structures on a category. We describe coherence constraints in terms of the cohomology of the corresponding operad. Our approach enables us to introduce the concept of coherence even for structures which are not given by commutative diagrams. In the second part of the paper we discuss ‘quantizations’ of various algebraic structures. We...

In the present paper we construct deformations of the Poincaré algebra as representations on a noncommutative spacetime with canonical commutation relations. These deformations are obtained by solving a set of conditions by an appropriate ansatz for the deformed Lorentz generator. They turn out to be Hopf algebras of quantum universal enveloping algebra type with nontrivial antipodes. In order ...

We establish a noncommutative analogue of the first fundamental theorem of classical invariant theory. For each quantum group associated with a classical Lie algebra, we construct a noncommutative associative algebra whose underlying vector space forms a module for the quantum group and whose algebraic structure is preserved by the quantum group action. The subspace of invariants is shown to fo...

In this paper we define and examine frame constructions for the family of many-valued modal logics introduced by M. Fitting in the ’90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting’s original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of ...

We construct a universal and even logically fully abstract realizability model for the sequential functional programming language of call-by-name FPC. This model is defined within the category of modest sets over the total combinatory algebra L of observational equivalence classes of closed terms of the untyped programming language λ+Error. This language is untyped lazy call-by-name lambda-calc...

It is well-known that the homology of the classifying space of the unitary group is isomorphic to the ring of symmetric functions Symm. We offer the cohomology of the space ΩΣCP as a topological model for the ring of quasisymmetric functions QSymm. We exploit standard results from topology to shed light on some of the algebraic properties of QSymm. In particular, we reprove the Ditters conjectu...

For any affine Weyl group, we introduce the pre-canonical bases. They are a set of bases {Ni}1?i?m+1 (where m is height highest root) spherical Hecke algebra that interpolates between standard basis N1 and canonical Nm+1. The expansion Ni+1 in terms Ni many cases very simple conjecture type A it positive.