相关论文: $\Ughr$ invariant quantization on some homogeneous…
This is a concise introduction to the theory of Lie groupoids, with emphasis in their role as models for stacks. After some preliminaries, we review the foundations on Lie groupoids, and we carefully study equivalences and proper groupoids.…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of…
A Poisson structure on a manifold is characterized by the Schouten bracket. The graded algebra of the tangent bundle with the Schouten bracket is a prototype of Lie superalgebra. The Poisson condition means that a cycle in the 2-chain…
In this paper, we classify the compact locally homogeneous non-gradient $m$-quasi Einstein 3-manifolds. Along the way, we prove that given a compact quotient of a Lie group of any dimension that is $m$-quasi Einstein, the potential vector…
Consider the quotient $G/B$ of a simple matrix Lie group $G$ by a subgroup $B$ isomorphic to a direct product of some of $S^1$s and $S^3$s such that its adjoint representation can be extended over $G$. Then it naturally inherits a stable…
We discuss a Moser type argument to show when a deformation of a Lie group homomorphism and of a Lie subgroup is trivial. For compact groups we obtain stability results.
We study the Poisson bracket invariant, which measures the level of Poisson noncommutativity of a smooth partition of unity, on closed symplectic surfaces. Motivated by a general conjecture of Polterovich and building on preliminary work of…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one…
Geometric quantization of a Poisson manifold need not imply quantization of its symplectic leaves. We provide the leafwise geometric quantization of a Poisson manifold, seen as a foliated one, whose quantum algebra restricted to each leaf…
Symplectic manifolds which are homogeneous spaces of Poisson-Lie groups are studied in this paper. We show that these spaces are, under certain assumptions, covering spaces of dressing orbits of the Poisson-Lie groups which act on them. The…
The paper investigates the (non)existence of compact quotients, by a discrete subgroup, of the homogeneous almost-complex strongly-pseudoconvex manifolds disconvered and classified by Gaussier-Sukhov and K.-H. Lee.
Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or…
Symmetries of Poisson manifolds are in general quantized just to symmetries up to homotopy of the quantized algebra of functions. It is therefore interesting to study symmetries up to homotopy of Poisson manifolds. We notice that they are…
We define and make initial study of Lie groupoids equipped with a compatible homogeneity (or graded bundle) structure, such objects we will refer to as weighted Lie groupoids. One can think of weighted Lie groupoids as graded manifolds in…
We obtain the Plancherel theorem for the quotient of a simple Lie group of real rank one by a convex-cocompact discrete subgroup and its consequences for the spectrum of locally invariant differential operators on bundles over Kleinian…
Let $X$ be a connected complex manifold equipped with a holomorphic action of a complex Lie group $G$. We investigate conditions under which a principal bundle on $X$ admits a $G$--equivariance structure.
We introduce the notion of Gamma-Lie bialgebra, where Gamma is a group. These objects give rise to cocommutative co-Poisson algebras, for which we construct quantization functors. This enlarges the class of co-Poisson algebras for which a…
We introduce a category composed of all quantizations of all Poisson algebras. By the category, we can treat in a unified way the various quantizations for all Poisson algebras and develop a new classical limit formulation. This formulation…