Results 1 to 10 of about 44 (44)

Gysin sequences and SU(2)‐symmetries of C∗‐algebras

Transactions of the London Mathematical Society, Volume 8, Issue 1, Page 440-492, December 2021., 2021
Abstract Motivated by the study of symmetries of C∗‐algebras, as well as by multivariate operator theory, we introduce the notion of an SU(2)‐equivariant subproduct system of Hilbert spaces. We analyse the resulting Toeplitz and Cuntz–Pimsner algebras and provide results about their topological invariants through Kasparov's bivariant K‐theory.
Francesca Arici, Jens Kaad
wiley   +1 more source

Yang–Baxter endomorphisms

Journal of the London Mathematical Society, Volume 103, Issue 2, Page 633-671, March 2021., 2021
Abstract Every unitary solution of the Yang–Baxter equation (R‐matrix) in dimension d can be viewed as a unitary element of the Cuntz algebra Od and as such defines an endomorphism of Od. These Yang–Baxter endomorphisms restrict and extend to several other C∗‐ and von Neumann algebras, and furthermore define a II1 factor associated with an extremal ...
Roberto Conti, Gandalf Lechner
wiley   +1 more source

On the homotopy type of L‐spectra of the integers

Journal of Topology, Volume 14, Issue 1, Page 183-214, March 2021., 2021
Abstract We show that quadratic and symmetric L‐theory of the integers are related by Anderson duality and that both spectra split integrally into the L‐theory of the real numbers and a generalised Eilenberg–Mac Lane spectrum. As a consequence, we obtain a corresponding splitting of the space G/Top. Finally, we prove analogous results for the genuine L‐
Fabian Hebestreit, Markus Land, Thomas Nikolaus   +2 more
wiley   +1 more source

F‐Manifolds and geometry of information

Bulletin of the London Mathematical Society, Volume 52, Issue 5, Page 777-792, October 2020., 2020
Abstract The theory of F‐manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and analytic geometry, at least since the 1990s. The focus of this paper consists in the demonstration that various
Noémie Combe, Yuri I. Manin
wiley   +1 more source

Quantum Dynamical Semigroups and Decoherence

Advances in Mathematical Physics, Volume 2011, Issue 1, 2011., 2011
We prove a version of the Jacobs‐de Leeuw‐Glicksberg splitting theorem for weak* continuous one‐parameter semigroups on dual Banach spaces. This result is applied to give sufficient conditions for a quantum dynamical semigroup to display decoherence. The underlying notion of decoherence is that introduced by Blanchard and Olkiewicz (2003).
Mario Hellmich, Christian Maes
wiley   +1 more source

Linear algebra and differential geometry on abstract Hilbert space

International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 14, Page 2241-2275, 2005., 2005
Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n‐dimensional vector spaces. However, while n‐dimensional spaces in applications are always realized as the Euclidean space Rn, Hilbert spaces admit various useful realizations as spaces of functions.
Alexey A. Kryukov
wiley   +1 more source

Exponentiating derivations of quasi ∗‐algebras: possible approaches and applications

International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 17, Page 2805-2820, 2005., 2005
The problem of exponentiating derivations of quasi ∗‐algebras is considered in view of applying it to the determination of the time evolution of a physical system. The particular case where observables constitute a proper CQ∗‐algebra is analyzed.
F. Bagarello, A. Inoue, C. Trapani
wiley   +1 more source

On Riemannian manifolds endowed with a locally conformal cosymplectic structure

International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 21, Page 3471-3478, 2005., 2005
We deal with a locally conformal cosymplectic manifold M(φ, Ω, ξ, η, g) admitting a conformal contact quasi‐torse‐forming vector field T. The presymplectic 2‐form Ω is a locally conformal cosymplectic 2‐form. It is shown that T is a 3‐exterior concurrent vector field. Infinitesimal transformations of the Lie algebra of ∧M are investigated.
Ion Mihai, Radu Rosca, Valentin Ghişoiu
wiley   +1 more source

Selberg′s trace formula on the k‐regular tree and applications

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 8, Page 501-526, 2003., 2003
We survey graph theoretic analogues of the Selberg trace and pretrace formulas along with some applications. This paper includes a review of the basic geometry of a k‐regular tree Ξ (symmetry group, geodesics, horocycles, and the analogue of the Laplace operator). A detailed discussion of the spherical functions is given.
Audrey Terras, Dorothy Wallace
wiley   +1 more source

The spectrum of a class of almost periodic operators

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 36, Page 2277-2301, 2003., 2003
For almost Mathieu operators, it is shown that the occurrence of Cantor spectrum and the existence, for every point in the spectrum and suitable phase parameters, of at least one localized eigenfunction which decays exponentially are inconsistent properties.
Norbert Riedel
wiley   +1 more source