Related papers: On centralizers in Azumaya domains

We compare modular forms of characteristic $p>0$ (i.e. Drinfeld's modular forms) and automorphic forms. We prove that spaces of these modular forms (which are of characteristic $p$) can be described by function spaces of characteristic…

Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.

In this paper the stable extended domain of a noncommutative rational function is introduced and it is shown that it can be completely described by a monic linear pencil from the minimal realization of the function. This result amends the…

Using ideas from automata theory we design a new efficient (deterministic) identity test for the \emph{noncommutative} polynomial identity testing problem (first introduced and studied in \cite{RS05,BW05}). We also apply this idea to the…

This paper develops the fundamentals of modular representation theory for finite monoids, introducing the decomposition matrix and exploring its connection to Brauer characters. We define modular characteristic and explain how the…

Let G be a connected, reductive group over an algebraically closed field of good characteristic. For u in G unipotent, we describe the conjugacy classes in the component group A(u) of the centralizer of u. Our results extend work of the…

In this paper, we consider a resource-consumer model taking into account a mutation effect between species (with constant mutation rate). The corresponding mutation operator is a discretization of the Laplacian in such a way that the…

In this article we prove a general result which in particular suggests that, on a simply connected domain in C, all the derivatives and anti-derivatives of the generic holomorphic function are unbounded. A similar result holds for the…

Let $p$ be a prime number. We consider diagonal $p$-permutation functors over a (commutative, unital) ring $\mathsf{R}$ in which all prime numbers different from $p$ are invertible. We first determine the finite groups $G$ for which the…

We develop a general theory of operator realizations, or ``linear representations" of analytic functions in several non-commuting variables about a matrix-centre. In particular we show that a non-commutative function has a matrix-centre…

The index of a finite-dimensional Lie algebra $g$ is the minimum of dimensions of stabilisers $g_\alpha$ of elements $\alpha\in g^*$. Let $g$ be a reductive Lie algebra and $z(x)$ a centraliser of a nilpotent element $x\in g$. Elashvili has…

We show that certain determinantal functions of multiple matrices, when summed over the symmetries of the cube, decompose into functions of the original matrices. These are shown to be true in complete generality; that is, no properties of…

Almkvist proved that for a commutative ring A the characteristic polynomial of an endomorphism \alpha:P \to P of a finitely generated projective A-module determines (P,\alpha) up to extensions. For a non-commutative ring A the generalized…

In this note we describe centralizers of Toeplitz operators with polynomial symbols on the Bergman space. As a consequence it is shown that if an element of the norm closed algebra generated by all Toeplitz operators commutes with a…

A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…

For $\kappa$ regular and uncountable we define variants of the classical cardinal characteristics modulo the non-stationary ideal.

It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. We give a new algorithm by evaluation and interpolation which is faster than…

The centralizer of a matrix in a full matrix algebra is called a principal centralizer matrix algebra. Characterizations are presented for principal centralizer matrix algebras to be Morita equivalent, almost $\nu$-stable derived…

Let X and Y be commuting nilpotent K-endomorphisms of a vector space V, where K is a field of characteristic p >= 0. If F=K(t) is the field of rational functions on the projective line, consider the K(t)-endomorphism A=X+tY of V. If p=0, or…

We show that mapping spaces in the p-local motivic stable category over an Fp-scheme are strictly commutative monoids (whence HZ-modules) in a canonical way.