Related papers: Fuzzy Riemann Surfaces
The resolvent algebra is a new C*-algebra of the canonical commutation relations of a boson field given by Buchholz-Grundling. We study analytic properties of quasi-free dynamics on the resolvent algebra. Subsequently we consider a…
In this paper we consider structures of complex Poisson brackets on the space of smooth functions in a $n$-dimensional complex manifold generated by the $(1,1)$-form $d=\partial+\overline{\partial}$-closed and non-degenerate (with…
We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…
We introduce fusion algebras with not necessarily positive structure constants and without identity element. We prove that they are semisimple when tensored with $\mathbb{C}$ and that their characters satisfy orthogonality relations. Then…
A $r$-parameter ${u}_{\{\kappa_1, \kappa_2, \cdots, \kappa_r\}}(2)$ algebra is introduced. Finite unitary representations are investigated. This polynomial algebra reduces via a contraction procedure to the generalized Weyl-Heisenberg…
By using C*-correspondences and Cuntz-Pimsner algebras, we associate to every subshift (also called a shift space) $X$ a C*-algebra $O_X$, which is a generalization of the Cuntz-Krieger algebras. We show that $O_X$ is the universal…
The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a…
We construct a representation of the braid groups in a cluster C*-algebra coming from a triangulation of the Riemann surface S with one or two cusps. It is shown that the Laurent polynomials attached to the K-theory of such an algebra are…
We study the semiclassical asymptotics of twisted algebras induced by symbol correspondences for quark systems ($SU(3)$-symmetric mechanical systems) as defined in our previous paper [3]. The linear span of harmonic functions on (co)adjoint…
In this paper we extend the standard differential geometric theory of Hamiltonian dynamics to noncommutative spaces, beginning with symplectic forms. Derivations on the algebra are used instead of vector fields, and interior products and…
We introduce two classes of algebras coming from partial triangulations of marked surfaces. The first one, called frozen algebra of a partial triangulation, is generally of infinite rank and contains frozen Jacobian algebras of…
Classical r-matrices of the three-dimensional real Lie bialgebras are obtained. In this way all three-dimensional real coboundary Lie bialgebras and their types (triangular, quasitriangular or factorizable) are classified. Then, by using…
We prove a quasi-Poisson bracket formula for the space of representations of the fundamental groupoid of a surface with boundary, which generalizes Goldman's Poisson bracket formula. We also deduce a similar formula for quasi-Poisson…
We introduce a family of compatible Poisson brackets on the space of $2\times 2$ polynomial matrices, which contains the reflection equation algebra bracket. Then we use it to derive a multi-Hamiltonian structure for a set of integrable…
Based on a new generalization of Cauchy-Riemann system presented in this paper, we introduce a class of quaternion-valued functions of a quaternionic variable, which are called algebraic regular functions. The set of algebraic regular…
The question studied here is the behavior of the Poisson bracket under C^0-perturbations. In this purpose, we introduce the notion of pseudo-representation and prove that for a normed Lie algebra, it converges to a representation. An…
We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…
We classify the centers of the quantized Weyl algebras that are PI and derive explicit formulas for the discriminants of these algebras over a general class of polynomial central subalgebras. Two different approaches to these formulas are…
To an $r$-dimensional subshift of finite type satisfying certain special properties we associate a $C^*$-algebra $\cA$. This algebra is a higher rank version of a Cuntz-Krieger algebra. In particular, it is simple, purely infinite and…
A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy…