Related papers: Coordinates for non-integrable Lie algebroids

Recently, we have constructed a non{linear (polynomial) extension of the 1-mode Heisenberg group and the corresponding Fock and Weyl representations. The transition from the 1-mode case to the current algebra level, in which the operators…

In this paper an automorphism of a unital C*-algebra is said to be /locally inner/ if on any element it agrees with some inner automorphism. We make a fairly complete study of local innerness in von Neumann algebras, incorporating…

In the setting of von Neumann algebras, measurable quantum groupoids have successfully been axiomatized and studied by Enock, Vallin, and Lesieur, whereas in the setting of $C^{*}$-algebras, a similar theory of locally compact quantum…

Lie theory for the integration of Lie algebroids to Lie groupoids, on the one hand, and of Poisson manifolds to symplectic groupoids, on the other, has undergone tremendous developements in the last decade, thanks to the work of…

In this paper, we introduce local expressions for discrete Mechanics. To apply our results simultaneously to several interesting cases, we derive these local expressions in the framework of Lie groupoids, following the program proposed by…

In this paper we continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm and we focus our attention on the so-called {\em locally convex…

We prove that the local (pseudo)group of biholomorphisms stabilizing a minimal, finitely nondegenerate real algebraic submanifold in C^n is a real algebraic local Lie group (the works of S.M. Baouendi, P. Ebenfelt, L.-P. Rothschild and D.…

Every partial algebra is the colimit of its total subalgebras. We prove this result for partial Boolean algebras (including orthomodular lattices) and the new notion of partial C*-algebras (including noncommutative C*-algebras), and…

The purpose of this paper is to propose a version of the notion of convenient Lie groupoid as a generalization of this concept in finite dimension. The authors point out which obstructions appear in the infinite dimensional context and how…

Motivated by a search for Lie group structures on groups of Poisson diffeomorphisms [24], we investigate linearizability of Poisson structures of Poisson groupoids around the unit section. After extending the Lagrangian neighbourhood…

The local multiplier C*-algebra M_{loc}(A) of any C*-algebra A can *-isomorphicly embedded into the injective envelope I(A) of A in such a way that the canonical embeddings of A into both these C*-algebras are identified. If A is…

Continuum Kac-Moody algebras have been recently introduced by the authors and O. Schiffmann. These are Lie algebras governed by a continuum root system, which can be realized as uncountable colimits of Borcherds-Kac-Moody algebras. In this…

All bialgebra structures for centrally extended Galilei algebra are classified. The corresponding Lie-Poisson structures on centrally extended Galilei group are found.

The theory of measured quantum groupoids, as defined by Lesieur and myself, was made to generalize the theory of quantum groups made by Kustarmans and Vaes, but was only defined in a von Neumann algebra setting; Th. Timmermann constructed…

We construct compact polyhedra with triangular faces whose links are generalized 3-gons. They are interesting compact spaces covered by Euclidean buildings of type $A_2$. Those spaces give us two-dimensional subshifts, which can be used to…

We introduce the concept of Roe C*-algebra for a locally compact groupoid whose unit space is in general not compact, and that is equipped with an appropriate coarse structure and Haar system. Using Connes' tangent groupoid method, we…

In this paper, the $C^*$-algebra of the seven-dimensional un-decomposable nilpotent Lie group is characterized explicitly for the first time(see \cite{chin}). Furthermore, the topology of its spectrum is described as a preparation for the…

In this paper we introduce the notion of generalized Lie algebroid and we develop a new formalism necessary to obtain a new solution for the Weistein's Problem. Many applications emphasize the importance and the utility of this new…

The dual Lie bialgebra of a certain ``quasitriangular'' Lie bialgebra structure on the Heisenberg Lie algebra determines a (non-compact) Poisson--Lie group G. The compatible Poisson bracket on G is non-linear, but it can still be realized…

Let $G$ be a locally compact group and $P \subset G$ be a closed Ore semigroup containing the identity element. Let $V: P \to B(\clh)$ be a representation such that for every $a \in P$, $V_{a}$ is an isometry and the final projections of…