Related papers: Quantum Ito B*-algebras, their Classification and …
We study (von Neumann) regular $^*$-subalgebras of $B(H)$, which we call R$^*$-algebras. The class of R$^*$-algebras coincides with that of "E$^*$-algebras that are pre-C$^*$-algebras" in the sense of Z. Sz\H{u}cs and B. Tak\'acs. We give…
We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns…
All coboundary Lie bialgebras and their corresponding Poisson--Lie structures are constructed for the oscillator algebra generated by $\{\aa,\ap,\am,\bb\}$. Quantum oscillator algebras are derived from these bialgebras by using the…
We present an explicit formula for the $K$-theory of the $C^*$-algebra associated with a relative generalized Boolean dynamical system $(\CB, \CL, \theta, \CI_\af; \CJ)$. In particular, we find concrete generators for the $K_1$-group of…
Previously we have shown that the topos approach to quantum theory of Doering and Isham can be generalised to a class of categories typically studied within the monoidal approach to quantum theory of Abramsky and Coecke. In the monoidal…
The quantum Ito formula has so far been proved for regular (bounded) quantum semimartingales We give three different extensions to classes of essentially self-adjoint (unbounded) quantum semimartingales. The first extension is to quantum…
We define the class of weakly approximately divisible unital C*-algebras and show that this class is closed under direct sums, direct limits, any tensor product with any C*-algebra, and quotients. A nuclear C*-algebra is weakly…
We give a detailed account of the cyclic $L_\infty$-algebra formulation of general relativity with cosmological constant in the Einstein-Cartan-Palatini formalism on spacetimes of arbitrary dimension and signature, which encompasses all…
We propose a notion of a quantum universal enveloping algebra for an arbitrary Lie algebra defined by generators and relations which is based on the quantum Lie operation concept. This enveloping algebra has a PBW basis that admits the…
Let X be a product system over a quasi-lattice ordered group. Under mild hypotheses, we associate to X a C*-algebra which is co-universal for injective Nica covariant Toeplitz representations of X which preserve the gauge coaction. Under…
We describe both the Bunce-Deddens C*-algebras and their Toeplitz versions, as crossed products of commutative C*-algebras by partial automorphisms. In the latter case, the commutative algebra has, as its spectrum, the union of the Cantor…
Quantization relates Poisson algebras to $C^*$-algebras. The analysis of local gauge symmetries in algebraic quantum field theory is approached through the quantization of classical gauge theories, regarded as constrained dynamical systems.…
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…
We prove that twisted groupoid C*-algebras are characterised, up to isomorphism, by having Cartan semigroups, a natural generalisation of normaliser semigroups of Cartan subalgebras. This extends the classic Kumjian-Renault theory to…
The classification of scalar Ito equations with a single noise source which admit a so called standard symmetry and hence are -- by the Kozlov construction -- integrable is by now complete. In this paper we study the situation, occurring in…
Since the seminal work of Wiener, the chaos expansion has evolved to a powerful methodology for studying a broad range of stochastic differential equations. Yet its complexity for systems subject to the white noise remains significant. The…
A tiling with infinite rotational symmetry, such as the Conway-Radin Pinwheel Tiling, gives rise to a topological dynamical system to which an \'etale equivalence relation is associated. A groupoid C*-algebra for a tiling is produced and a…
It is shown that introducing the quantum effects using deBroglie--Bohm theory in the canonical formulation of gravity would change the constraints algebra. The new algebra is derived and shown that it is the clear projection of general…
We exhibit a countably infinite family of simple, separable, nuclear, and mutually non-isomorphic C*-algebras which agree on K-theory and traces. The algebras do not absorb the Jiang-Su algebra Z tensorially, answering a question of N. C.…
A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…