Related papers: Bergman's Centralizer Theorem and quantization

The aim of the note is to provide an introduction to the algebraic, geometric and quantum field theoretic ideas that lie behind the Kontsevich-Cattaneo-Felder formula for the quantization of Poisson structures. We show how the quantization…

We use operator algebras and operator theory to obtain new result concerning Berezin quantization of compact K\"ahler manifolds. Our main tool is the notion of subproduct systems of finite-dimensional Hilbert spaces, which enables all…

A weak version of Birkhoff's generalization of the Perron-Frobenius theorem states that every endomorphism of a finite-dimensional real vector that leaves invariant a non-degenerate closed convex cone has an eigenvector in that cone. Here,…

We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials, and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves…

As is known, every finite-dimensional algebra over a field is isomorphic to the centralizer algebra of \textbf{two} matrices. So it is fundamental to study first the centralizer algebra of a single matrix, called a centralizer matrix…

We consider properties of polynomials with coefficients in division rings. A theorem on the decomposition of a polynomial with coefficients in an arbitrary division ring is obtained. It is shown that if a non-central element is not a root…

Let ${\mathscr G}$ be a linear algebraic group over $k$, where $k$ is an algebraically closed field, a pseudo-finite field or the valuation ring of a nonarchimedean local field. Let $G= {\mathscr G}(k)$. We prove that if $\gamma, \delta\in…

We prove that centralizers of elements in [f.g. free]-by-cyclic groups are computable. As a corollary we get that, given two conjugate elements in a [f.g. free]-by-cyclic group, the set of conjugators can be computed and that the conjugacy…

Fix a commutative ring $\mathbf{k}$, two elements $\beta,\alpha\in\mathbf{k}$ and a positive integer $n$. Let $\mathcal{X}$ be the polynomial ring over $\mathbf{k}$ in the $n(n-1)/2$ indeterminates $x_{i,j}$ for all $1\leq i<j\leq n$.…

For a simple linear algebraic group $G$, the chiral universal centralizer $\mathbf{I}_{G,k}$ is a vertex operator algebra, which is the chiralization of the universal centralizer $\mathfrak{Z}_G$. The variety $\mathfrak{Z}_G$ is identified…

A linear mapping $\phi$ on an algebra $\mathcal{A}$ is called a centralizable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B=A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$, and $\phi$ is called a derivable mapping at…

For an endomorphism f\inEnd{M) of a left R-module M we investigate the structure and the polynomial identities of the zero-level centralizer Cen_0(f) and the factor Cen(f)/Cen_0(f). A double zero-centralizer theorem for Cen_0(Cen_0(f)) is…

Let $D$ be division algebra over its center $C$, let $\sigma$ be an endormorphism of $D$, let $\delta$ be a left $\sigma$-derivation of $D$, and let $R=D[t;\sigma,\delta]$ be a skew polynomial ring. We study the structure of a class of…

In this paper we consider images of (ordinary) noncommutative polynomials on matrix algebras endowed with a graded structure. We give necessary and sufficient conditions to verify that some multilinear polynomial is a central polynomial, or…

Finsler's Lemma charactrizes all pairs of symmetric $n \times n$ real matrices $A$ and $B$ which satisfy the property that $v^T A v>0$ for every nonzero $v \in \mathbb{R}^n$ such that $v^T B v=0$. We extend this characterization to all…

Let $f \in \mathbb{R}[x]$ be a polynomial with real coefficients. We say that $f$ is eventually non-negative if $f^m$ has non-negative coefficients for all sufficiently large $m \in \mathbb{N}$. In this short note, we give a classification…

Let $K$ be a field of characteristic zero, let $\sigma$ be an automorphism of $K$ and let $\delta$ be a $\sigma$-derivation of $K$. We show that the division ring $D=K(x;\sigma,\delta)$ either has the property that every finitely generated…

We study the centralizer of a parabolic subalgebra in the Hecke algebra associated with an arbitrary (possibly infinite) Coxeter group. While the center and cocenter have been extensively studied in the finite and affine cases, much less is…

We study the Hall and composition algebras of an affine quiver. In the case of a cyclic quiver, we provide generators for the central polynomial algebra described by Schiffmann and prove that this is in fact the whole of the centre of the…

We consider the Graver basis, the universal Groebner basis, a Markov basis and the set of the circuits of a toric ideal. Let $A, B$ be any two of these bases such that $A\not \subset B$, we prove that there is no polynomial on the size or…