相关论文: Poisson Diffeomorphism Groups

This paper develops new aspects of the interplay between shifted symplectic geometry and classical Poisson geometry, focusing on lagrangian morphisms into 2-shifted symplectic groups. We establish a Lie-type correspondence between such…

In this survey, we discuss a series of linearization problems--for Poisson structures, Lie algebroids, and Lie groupoids. The last problem involves a conjecture on the structure of proper groupoids. Attempting to prove this by the method of…

We consider some differential geometric classes of local and nonlocal Poisson and symplectic structures on loop spaces of smooth manifolds which give natural Hamiltonian and multihamiltonian representations for some important nonlinear…

We introduce a new type of noncommutative Poisson structure on associative algebras. It induces Poisson structures on the moduli spaces classifying semisimple modules. Path algebras of doubled quivers and preprojective algebras have…

It is shown that the new formula for the field theory Poisson brackets arise naturally in the extension of the formal variational calculus incorporating divergences. The linear spaces of local functionals, evolutionary vector fields,…

We introduce a concise quantum operator formula for bosonization in which the Lie group structure appears in a natural way. The connection between fermions and bosons is found to be exactly the connection between Lie group elements and the…

We introduce and study some mixed product Poisson structures on product manifolds associated to Poisson Lie groups and Lie bialgebras. For quasitriangular Lie bialgebras, our construction is equivalent to that of fusion products of…

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…

This thesis studies normal forms for Poisson structures around symplectic leaves using several techniques: geometric, formal and analytic ones. One of the main results (Theorem 2) is a normal form theorem in Poisson geometry, which is the…

We consider contractions of Lie and Poisson algebras and the behaviour of their centres under contractions. A polynomial Poisson algebra A=K[W] is said to be of Kostant type, if its centre Z(A) is freely generated by homogeneous polynomials…

Several types of generically-nondegenerate Poisson structures can be effectively studied as symplectic structures on naturally associated Lie algebroids. Relevant examples of this phenomenon include log-, elliptic, $b^k$-, scattering and…

We construct local bihamiltonian structures from classical $W$-algebras associated to non-regular nilpotent elements of regular semisimple type in Lie algebras of type $A_2$ and $A_3$. They form exact Poisson pencil, admit a dispersionless…

This paper investigates the geometric and algebraic interplay between F-manifolds and a newly defined class of structures termed F$_\text{man}$-algebras. We specialize our study to the category of F-Lie groups, characterized by a Lie group…

We consider the Lie group of smooth diffeomorphisms Diff$(M)$ of a simple polytope $M$ in the euclidean space. Simple polytopes are special cases of manifolds with corners. The geometric setting allows to study in particular, the subgroup…

We construct a smooth Lie group structure on the group of real analytic diffeomorphisms of a compact analytic manifold with corners. This generalises the known analogous results in the situation where the real analytic manifold has no…

This paper develops a graphical calculus to determine the $n$-shifted Poisson structures on finitely generated semi-free commutative differential graded algebras. When applied to the Chevalley-Eilenberg algebra of an ordinary Lie algebra,…

We study the transverse Poisson structure to adjoint orbits in a complex semi-simple Lie algebra. The problem is first reduced to the case of nilpotent orbits. We prove then that in suitably chosen quasi-homogeneous coordinates the…

After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologies on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and…

We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means of the adjoint representations of Lie algebras. In this way, we calculate some compatible Poisson structures on four dimensional and…

Let $R$ be a commutative ring that is free of rank $k$ as an abelian group, $p$ a prime, and $SL(n,R)$ the special linear group. We show that the Lie algebra associated to the filtration of $SL(n,R)$ by $p$-congruence subgroups is…