Related papers: Algebras and their Covariant representations in qu…
We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…
The quantal algebra combines classical and quantum mechanics into an abstract structurally unified structure. The structure uses two products: one symmetric and one anti-symmetric. The local structure of spacetime is contained in the…
This paper introduces a systematic algorithm for deriving a new unitary representation of the Lorentz algebra ($so(1,3)$) and an irreducible unitary representation of the extended (anti) de-Sitter algebra ($so(2,4)$) on…
The coexistence relation of quantum effects is a fundamental structure, describing those pairs of experimental events that can be implemented in a single setup. Only in the simplest case of qubit effects an analytic characterization of…
Classically the constraint algebra of general relativity, which generates gauge transformations, is equivalent to spacetime covariance. In LQG, inverse triad corrections lead to an effective Hamiltonian constraint which can lead to a…
The Lie-Rinehart algebra of a manifold M, defined by the Lie structure of the vector fields, their action and their module structure on the infinitely differentiable functions on M, is a common, diffeomorphism invariant, algebra for both…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
In this paper, we introduce the notion of multiplier of a Hilbert algebra. The space of bounded multipliers is a semifinite von Neumann algebra isomorphic to the left von Neumann algebra of the Hilbert algebra, as expected. However, in the…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
This note aims to investigate the tensor product of two given Hilbert quasi *-algebras and its properties. The construction proposed in this note turns out to be again a Hilbert quasi *-algebra, thus interesting representability properties…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
We introduce unbounded strongly irreducible operators and transitive operators. These operators are related to a certain class of indecomposable Hilbert representations of quivers on infinite-dimensional Hilbert spaces. We regard the theory…
We consider a family of Hecke C*-algebras which can be realised as crossed products by semigroups of endomorphisms. We show by dilating representations of the semigroup crossed product that the category of representations of the Hecke…
In this work we explore the structure of Clifford algebras and the representations of the algebraic spinors in quantum information theory. Initially we present an general formulation through elements of left minimal ideals in tensor…
Clifford algebras are important structures in Geometric Algebra and Quantum Mechanics. They have allowed a formalization of the primitive operators in Quantum Theory. The algebras are built over vector spaces with dimension a power of 2…
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…
We introduce an equivariant algebraic kk-theory for G-algebras and G-graded algebras. We study some adjointness theorems related with crossed product, trivial action, induction and restriction. In particular we obtain an algebraic version…
We investigate commutative analogues of Clifford algebras -- algebras whose generators square to $\pm1$ but commute, instead of anti-commuting as they do in Clifford algebras. We observe that commutativity allows for elegant results. We…
The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…