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We associate with the ring $R$ of algebraic integers in a number field a C*-algebra $\cT[R]$. It is an extension of the ring C*-algebra $\cA[R]$ studied previously by the first named author in collaboration with X.Li. In contrast to…

Theta functions play a major role in many current researches and are powerful tools for studying integrable systems. The purpose of this paper is to provide a short and quick exposition of some aspects of meromorphic theta functions for…

Suppose that a locally compact group $G$ acts freely and properly on the right of a locally compact space $T$. Rieffel proved that if $\alpha$ is an action of $G$ on a $C^*$-algebra $A$ and there is an equivariant embedding of $C_0(T)$ in…

Let G and H be two locally compact groups acting on a C*-algebra A by commuting actions. We construct an action on the crossed product AXG out of a unitary 2-cocycle u and the action of H on A. For A commutative, and free and proper actions…

We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of…

We derive explicit formulas for the action of the Hecke operator $T(p)$ on the genus theta series of a positive definite integral quadratic form and prove a theorem on the generation of spaces of Eisenstein series by genus theta series. We…

We construct a differential operator on sheaves of $p$-adic modular forms defined over the locus of $p$-rank $\ge 1$ of the Siegel threefold, by applying a revisited version of the approach that Sean Howe recently introduced in his paper "A…

Using duality and topological theory of well behaved Hopf algebras (as defined in [2]) we construct star-product models of non compact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple…

We describe explicitly a noncommutative deformation of the *-algebra of functions on the Teichm\"uller space of Riemann surfaces with holes equivariant w.r.t. the mapping class group action.

We investigate the structure of circle actions with the Rokhlin property, particularly in relation to equivariant $KK$-theory. Our main results are $\mathbb{T}$-equivariant versions of celebrated results of Kirchberg: any Rokhlin action on…

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways. The first…

Consider a spin manifold M, equipped with a line bundle L and an action of a compact Lie group G. We can attach to this data a family Theta(k) of distributions on the dual of the Lie algebra of G. The aim of this paper is to study the…

Let $A=\underrightarrow{\lim}{A_n}$ be an AF algebra, $G$ be a compact group. We consider inductive limit actions of the form $\alpha=\underrightarrow{\lim}{\alpha_n}$, where $\alpha_n\colon G\curvearrowright A_n$ is an action on the finite…

We consider an action of the real line on a C*-algebra for which there is a centre-valued invariant trace. We define a family of Toeplitz operators with symbols in the original algebra. When the symbol is invertible, the Toeplitz operator…

Let $A$ be a star product on a symplectic manifold $(M,\omega_0)$, $\frac{1}{t}[\omega]$ its Fedosov class, where $\omega$ is a deformation of $\omega_0$. We prove that for a complex polarization of $\omega$ there exists a commutative…

This paper has two parts. The first part is a review and extension of the methods of integration of Leibniz algebras into Lie racks, including as new feature a new way of integrating 2-cocycles (see Lemma 3.9). In the second part, we use…

Let $R$ be a commutative ring with identity and let $V$ be a free $R$-module of rank $n$ for some $n\in\mathbb{N}$. Fixing an $R$-basis $\mathcal{E}$ of $V$, the symmetric group $\mathfrak{S}_n$ acts on $V$ by permuting $\mathcal{E}$ and…

Given an n x n integer matrix A whose eigenvalues are strictly greater than 1 in absolute value, let \sigma_A be the transformation of the n-torus T^n=R^n/Z^n defined by \sigma_A(e^{2\pi ix})=e^{2\pi iAx} for x\in R^n. We study the…

Based on work done by Bonechi, Cattaneo, Felder and Zabzine on Poisson sigma models, we formally show that Kontsevich's star product can be obtained from the twisted convolution algebra of the geometric quantization of a Lie 2-groupoid, one…

For an action $\alpha$ of a group $G$ on an algebra $R$ (over $\Bbb C$), the crossed product $R\times_\alpha G$ is the vector space of $R$-valued functions with finite support in $G$, together with the twisted convolution product given by…