相关论文: Universal lifting theorem and quasi-Poisson groupo…

Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately…

We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of our construction of the formality quasi-isomorphism is…

This work is motivated by the search for an "explicit" proof of the Bloch-Kato conjecture in Galois cohomology, proved by Voevodsky. Our concern here is to lay the foundation for a theory that, we believe, will lead to such a proof- and to…

We prove that under certain mild assumptions a Lie bialgebroid integrates to a Poisson groupoid. This includes, in particular, a new proof of the existence of local symplectic groupoids for any Poisson manifold, a theorem of Karasev and of…

A universal category-theoretical characterization of groupoid equivariant $KK^G$-theory for ${\mathbb{Z}}_2$-graded $C^*$-algebras is established, by observing the ``$KK$-axiom'' that for each $[s,{\cal E} \oplus B, \mathbb{F}] \in…

We prove the Andruskiewitsch-Dumas conjecture that the automorphism group of the positive part of the quantized universal enveloping algebra $U_q({\mathfrak{g}})$ of an arbitrary finite dimensional simple Lie algebra g is isomorphic to the…

We introduce the universal unitarily graded A-algebra for a commutative ring A and an arbitrary abelian extension U of the group of units of A, and use this concept to give simplified proofs of the main theorems of co-Galois theory in the…

A unitary representation of a, possibly infinite dimensional, Lie group G is called semi-bounded if the corresponding operators id\pi(x) from the derived representations are uniformly bounded from above on some non-empty open subset of the…

We deal with a Lie group G acting by isometries on a Riemannian manifold M, such that the quotient M/G is an orbifold, or, equivalently, all slice representations are polar. We show that any smooth orbifold symmetric 2-tensor on M/G lifts…

In this paper, we consider Lie algebroids over commutative ringed spaces. Lie algebroids over ringed spaces unify the existing notion of Lie algebroids over smooth manifolds, complex manifolds, analytic spaces, algebraic varieties, and…

In recent years methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this note it is shown that the latter method is actually…

The following homotopy lifting theorem is proved: Let $\phi, \psi: B \to D/I$ be homotopic $\ast$-homomorphisms and suppose $\psi$ lifts to a (discrete) asymptotic homomorphism. Then $\phi$ lifts to a (discrete) asymptotic homomorphism.…

Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by Drinfeld. To any Lie quasi-bialgebra structure of finite-dimensional (G, \mu, \gamma ,\phi ?), correspond one Lie algebra structure on D = G\oplus G*, called…

It is expected that the periodic cyclic homology of a DG algebra over the field of complex numbers (and, more generally, the periodic cyclic homology of a DG category) carries a lot of additional structure similar to the mixed Hodge…

Let $\{\phi_s\}_{s\in S}$ be a commutative semigroup of completely positive, contractive, and weak*-continuous linear maps acting on a von Neumann algebra $N$. Assume there exists a semigroup $\{\alpha_s\}_{s\in S}$ of weak*-continuous…

Double (quasi-)Poisson brackets were introduced on associative algebras by Van den Bergh to induce a (quasi-)Poisson structure on their representation spaces naturally equipped with a $\mathrm{GL}$-action (type $\mathtt{A}$). If there…

In this paper, we introduce the notion of differential graded Poisson algebra and study its universal enveloping algebra. From any differential graded Poisson algebra $A$, we construct two isomorphic differential graded algebras: $A^e$ and…

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…

Essentially generalizing Lie's results, we prove that the contact equivalence groupoid of a class of (1+1)-dimensional generalized nonlinear Klein-Gordon equations is the first-order prolongation of its point equivalence groupoid, and then…

The author, and independently De Concini, conjectured that the monodromy of the Casimir connection of a simple Lie algebra g is described by the quantum Weyl group operators of the quantum group U_h(g). The aim of this paper, and of its…