Related papers: A model theoretic Rieffel's theorem of quantum 2-t…
The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter theta (in appropriate units): an isomorphism is established between an abelian noncommutative…
We point out a connection between Gabor analysis and noncommutative analysis. Especially, the strong Morita equivalence of noncommutative tori appears as underlying setting for Gabor analysis, since the construction of equivalence bimodules…
We investigate a set of functional equations defining a projection in the noncommutative 2-torus algebra $A_{\theta}$. The exact solutions of these provide various generalisations of the Powers-Rieffel projection. By identifying the…
We consider the compactification M(atrix) theory on a Riemann surface Sigma of genus g>1. A natural generalization of the case of the torus leads to construct a projective unitary representation of pi_1(\Sigma), realized on the Hilbert…
We study the Morita equivalence for field theories on noncommutative two-tori. For rational values of the noncommutativity parameter $\theta $ (in appropriate units) we show the equivalence between an abelian noncommutative field theory and…
We investigate field theories on the non-commutative torus upon varying theta, the parameter of non-commutativity. We argue that one should think of Morita equivalence as a symmetry of algebras describing the same space rather than of…
In the present investigation we are linking noncommutative geometry over noncommutative tori with Gabor analysis, where the first has its roots in operator algebras and the second in time-frequency analysis. Therefore we are in the position…
We give a local expression for the {\it scalar curvature} of the noncommutative two torus $ A_{\theta} = C(\mathbb{T}_{\theta}^2)$ equipped with an arbitrary translation invariant complex structure and Weyl factor. This is achieved by…
It was shown by A. Connes, M. Douglas and A. Schwarz that noncommutative tori arise naturally in consideration of toroidal compactifications of M(atrix) theory. A similar analysis of toroidal Z_{2} orbifolds leads to the algebra B_{\theta}…
We classify instances of quantum pseudo-telepathy in the graph isomorphism game, exploiting the recently discovered connection between quantum information and the theory of quantum automorphism groups. Specifically, we show that graphs…
We introduce an operator-algebraic framework for Morita equivalence of quantum graphs based on $\Delta$-equivalence of operator systems introduced by Eleftherakis, Kakariadis and Todorov. Adopting the perspective of Weaver, we view quantum…
One can describe an $n$-dimensional noncommutative torus by means of an antisymmetric $n\times n$-matrix $\theta$. We construct an action of the group $SO(n,n|\bf Z)$ on the space of antisymmetric matrices and show that, generically,…
In this paper, we will introduce Quantum Toric Varieties which are (non-commutative) generalizations of ordinary toric varieties where all the tori of the classical theory are replaced by quantum tori. Quantum toric geometry is the…
We describe a structure over the complex numbers associated with the non-commutative algebra Aq called quantum 2-tori. These turn out to have uncountably categorical L_omega1,omega-theory, and are similar to other pseudo-analytic structures…
2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a…
We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need…
It was shown by Connes, Douglas, Schwarz[1] that one can compactify M(atrix) theory on noncommutative torus. We prove that compactifications on Morita equivalent tori are physically equivalent. This statement can be considered as a…
We show that the Quantum Isometry Group(as introduced in \cite{goswami}) of the n tori is the classical isometry group. Moreover, using a result in \cite{bhowmick goswami}, we conclude that the Quantum Isometry group of the noncommutative n…
The "noncommutative geometry" of complex algebraic curves is studied. As first step, we clarify a morphism between elliptic curves, or complex tori, and C*-algebras T_t={u,v | vu=exp(2\pi it)uv}, or noncommutative tori. The main result says…
We prove the analogue of the Riemann-Roch formula for the noncommutative two torus $ A_{\theta} = C(\mathbb{T}_{\theta}^2)$ equipped with an arbitrary translation invariant complex structure and a Weyl factor represented by a positive…