Related papers: Poisson Centralizer of the Trace

We determine all restrictions on the dimension of the fixed locus of a diagonalizable group acting on a smooth projective variety that arise from the Chern numbers of the ambient variety. We reduce the problem to finding lower bounds for…

A Poisson system is a Poisson point process and a group action, together forming a measure-preserving dynamical system. Ornstein and Weiss proved Poisson systems over many amenable groups were isomorphic in their 1987 paper. We consider…

A general approach is proposed to constructing covariant Poisson brackets in the space of histories of a classical field-theoretical model. The approach is based on the concept of Lagrange anchor, which was originally developed as a tool…

We show that the centralizer of a nonscalar element in the coproduct $k\langle X\rangle *k[Y]$ of a free associative algebra and a polynomial algebra over a given field is commutative. For $k\langle X \rangle$ this is part of Bergman's…

Meta-centralizers of non-locally compact group algebras are studied. Theorems about their representations with the help of families of generalized measures are proved. Isomorphisms of group algebras are investigated in relation with…

The central force problem is considered in a three dimensional space in which the Poisson bracket among the spatial coordinates is the one by the SU(2) Lie algebra. It is shown that among attractive power-law potentials it is only the…

Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the…

This work takes place over a conformally flat spin manifold (M,g). We prove existence and uniqueness of the conformally equivariant quantization valued in spinor differential operators, and provide an explicit formula for it when restricted…

We study the semi-classical trace formula at a critical energy level for a $h$-pseudo-differential operator whose principal symbol has a unique non-degenerate critical point for that energy. This leads to the study of Hamiltonian systems…

In the canonical formulation of a classical field theory, symmetry properties are encoded in the Poisson bracket algebra, which may have a central term. Starting from this well understood canonical structure, we derive the related…

We investigate the structure of the centralizer and the normalizer of a local analytic or formal differential system at a nondegenerate stationary point, using the theory of Poincar\'e-Dulac normal forms. Our main results are concerned with…

Olshanski's centralizer construction provides a realization of the Yangian for the Lie algebra gl(n) as a subalgebra in the projective limit of a chain of centralizers in the universal enveloping algebras. We give a modified version of this…

Let $p$ be a an odd prime and let $G$ be a finite $p$-group with cyclic commutator subgroup $G'$. We prove that the exponent and the abelianization of the centralizer of $G'$ in $G$ are determined by the group algebra of $G$ over any field…

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…

This paper consists of two parts. In the first part we show that any Poisson algebraic group over a field of characteristic zero and any Poisson Lie group admits a local quantization. This answers positively a question of Drinfeld. In the…

Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among…

We determine the centralizers of certain isomorphic copies of spin subalgebras $\mathfrak{spin}(r)$ in $\mathfrak{so}(d_rm)$, where $d_r$ is the dimension of a real irreducible representation of $Cl_r^0$, the even Clifford algebra…

We develop a Poisson geometric framework for studying the representation theory of all contragredient quantum super groups at roots of unity. This is done in a uniform fashion by treating the larger class of quantum doubles of bozonizations…

Cohomology spaces of the Poisson superalgebra realized on smooth Grassmann-valued functions with compact support on $R^{2n}$ ($C^{2n}) are investigated under suitable continuity restrictions on cochains. The first and second cohomology…

Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson structure, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A general theory of the…