Results 41 to 50 of about 39,950 (199)

Nilpotent elements and Armendariz rings

Journal of Algebra, 2008
Let \(R\) denote an associative ring with \(1\), and let \(\text{nil}(R)\) denote the set of nilpotent elements. Further, let \(f(x)=\sum_{i=0}^ma_ix^i,g(x)=\sum_{j=0}^nb_jx^j\in R[x]\) denote two arbitrary polynomials. One says that \(R\) is an Armendariz ring if \(f(x)g(x)=0\) implies that \(a_ib_j=0\) for all \(i\) and \(j\).
openaire   +1 more source

W-algebras at the critical level

, 2011
Let g be a complex simple Lie algebra, f a nilpotent element of g. We show that (1) the center of the W-algebra $W^{cri}(g,f)$ associated with (g,f) at the critical level coincides with the Feigin-Frenkel center of the affine Lie algebra associated with ...
Arakawa, Tomoyuki
core   +1 more source

m-rnc rings [PDF]

BIO Web of Conferences
In this article, an element w of an associative ring R is called m-regular nil clean or m-rnc if expressed as w = am + b where am is m-regular element and b is a nilpotent element. R is named m-regular nil clean ring or m-rnc ring. If all the elements of
Mahmood Ali Sh., Mohammed Ibraheem Zubaida   +1 more
doaj   +1 more source

Nilpotent Elements in Lie Algebras

Journal of Algebra, 1990
A classical result of \textit{Fine} and \textit{Herstein} is that the number of n by n nilpotent matrices with entries in GF(q) is a power of q, that power being \(n^ 2-n\). Kaplansky formulates an analogous problem in Lie algebras as follows: For a simple Lie algebra L of n by n matrices with entries from a field of q elements, is the number of ...
openaire   +1 more source

The Natural Components of a Regular Linear System

Oxford Bulletin of Economics and Statistics, EarlyView.
ABSTRACT The analysis of a finite‐dimensional regular linear system may be simplified by separating the system into its natural components. The natural components are smaller linear systems on separate subspaces whose dimensions sum to the dimension of the original linear system.
Brendan K. Beare, Phil Howlett
wiley   +1 more source

Lipschitz groups and Lipschitz maps [PDF]

International Journal of Group Theory, 2017
‎‎This contribution mainly focuses on some aspects of Lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with Lipschitz multiplication and inversion map‎. ‎In the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be ...
Laurent Poinsot
doaj   +1 more source

Solvable Lie algebras with Borel nilradicals

, 2012
The present article is part of a research program the aim of which is to find all indecomposable solvable extensions of a given class of nilpotent Lie algebras.
Snobl, Libor, Winternitz, Pavel
core   +1 more source

Coulomb branch algebras via symplectic cohomology

Journal of Topology, Volume 19, Issue 2, June 2026.
Abstract Let (M¯,ω)$(\bar{M}, \omega)$ be a compact symplectic manifold with convex boundary and c1(TM¯)=0$c_1(T\bar{M})=0$. Suppose that (M¯,ω)$(\bar{M}, \omega)$ is equipped with a convex Hamiltonian G$G$‐action for some connected, compact Lie group G$G$.
Eduardo González, Cheuk Yu Mak, Dan Pomerleano   +2 more
wiley   +1 more source

A Remark on Quadrics in Projective Klingenberg Spaces over a Certain Local Algebra

Mathematics, 2020
This article is devoted to some polar properties of quadrics in the projective Klingenberg spaces over a local ring which is a linear algebra generated by one nilpotent element.
Marek Jukl
doaj   +1 more source

An extended definition of Anosov representation for relatively hyperbolic groups

Journal of Topology, Volume 19, Issue 2, June 2026.
Abstract We define a new family of discrete representations of relatively hyperbolic groups which unifies many existing definitions and examples of geometrically finite behavior in higher rank. The definition includes the relative Anosov representations defined by Kapovich–Leeb and Zhu, and Zhu–Zimmer, as well as holonomy representations of various ...
Theodore Weisman
wiley   +1 more source