Related papers: Noncommutative Symmetric Functions Associated with…
We discuss the possibility to represent smooth nonnegative matrix-valued functions as finite linear combinations of fixed matrices with positive real-valued coefficients whose square roots are Lipschitz continuous. This issue is reduced to…
We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation free infinite divisibility * free and strong cancellation of…
We define a free holomorphic function to be a function that is locally a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization…
We develop the analogue of the Witt construction in characteristic one. We construct a functor from pairs of a perfect semi-ring of characteristic one and an element strictly larger than one, to real Banach algebras. We find that the…
To a planar algebra P in the sense of Jones we associate a natural non- commutative ring, which can be viewed as the ring of non-commutative polynomials in several indeterminates, invariant under a symmetry encoded by P. We show that this…
Associated to a simple root of a finite-dimensional complex semisimple Lie algebra, there are several endofunctors (defined by Arkhipov, Enright, Frenkel, Irving, Jantzen, Joseph, Mathieu, Vogan and Zuckerman) on the BGG category…
In this article, we describe the endomorphism ring of a finitely generated progenerator module of a weighted Leavitt path algebra $L_{K}(E, w)$ of a finite vertex weighted graph $(E, w)$. Contrary to the case of Leavitt path algebras, we…
In our previous work [math-ph/9904020], we proved that the correlation functions for simultaneous zeros of random generalized polynomials have universal scaling limits and we gave explicit formulas for pair correlations in codimensions 1…
We discuss the folklore construction of the Gray tensor product of 2-categories as obtained by factoring the map from the funny tensor product to the cartesian product. We show that this factorisation can be obtained without using a…
The article presents various Witt type vector field realizations of 2-D Cayley-Klein algebras with non-vanishing curvatures. The expressions of the vector fields involve Jacobi elliptic functions whose moduli are directly related to the…
The Ginsparg-Wilson relation is extended to interacting field theories with general linear symmetries. Our relation encodes the remnant of the original symmetry in terms of the blocked fields and guides the construction of invariant lattice…
A linear system of real quadratic forms defines a real projective variety. The real non-singular locus of this variety (more precisely of the underlying scheme) has a highly connected double cover as long as each non-zero form in the system…
We construct $\mathbb{Z}_p$-lattices and $\mathbb{F}_q[\![t]\!]$-lattices from cyclic $(f,\sigma)$-codes over finite chain rings, employing quotients of natural nonassociative orders and principal left ideals in carefully chosen…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
Given a finite associative ring with unity, $R$, and its two-dimensional left module, $^{2}R$, the following two problems are addressed: 1) the existence of vectors of $^{2}R$ that do not belong to any free cyclic submodule (FCS) generated…
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of…
The noncommutative symmetric functions $\textbf{NSym}$ were first defined abstractly by Gelfand et al. in 1995 as the free associative algebra generated by noncommuting indeterminants $\{\boldsymbol{e}_n\}_{n\in \mathbb{N}}$ that were taken…
Zeros of entire functions can be found using either the Fourier methods of Riemann-Polya or the Generalized Gamma Convolution (GGC) methods of Thorin-Bondesson. This connection is based on a duality between the Hadamard-Weierstrass…
A free resolution of free partially commutative monoids is constructed and with its help the homological dimension of these monoids is calculated.
In Noncommutative Geometry, as in quantum theory, classically real variables are assumed to correspond to self-adjoint operators. We consider the relaxation of the requirement of self-adjointness to mere symmetry for operators $X_i$ which…