Search results for "Jordan"
showing 10 items of 59 documents
Multialternating Jordan polynomials and codimension growth of matrix algebras
2007
Abstract Let R be the Jordan algebra of k × k matrices over a field of characteristic zero. We exhibit a noncommutative Jordan polynomial f multialternating on disjoint sets of variables of order k 2 and we prove that f is not a polynomial identity of R . We then study the growth of the polynomial identities of the Jordan algebra R through an analysis of its sequence of Jordan codimensions. By exploiting the basic properties of the polynomial f , we are able to prove that the exponential rate of growth of the sequence of Jordan codimensions of R in precisely k 2 .
Izrael a Palestyńczycy. Wojna i okupacja jako rozwiązanie?
2015
Celem artykułu jest szkic analizy konfliktu izraelsko-palestyńskiego, zwłaszcza w kontekście sposobu radzenia sobie przez państwo żydowskie z palestyńskim ruchem narodowowyzwoleńczym. W pierwszej części zwrócono uwagę na specyficzne okoliczności powstania Izraela – państwo to miejscowa ludność arabska uznała za ostatni europejski projekt kolonialny. Następnie opisano tak zwaną matrycę kontroli nad Palestyńczykami, którą zaprezentował antropolog i aktywista pokojowy Jeff Halper. W ostatniej części skupiono się na Operacji Ochronny Brzeg i jej ofiarach, głównie palestyńskich cywilach. Artykuł kończy się wskazaniem dwóch generalnych kierunków, w których może ewoluować opisywany konflikt.
Varieties of special Jordan algebras of almost polynomial growth
2019
Abstract Let J be a special Jordan algebra and let c n ( J ) be its corresponding codimension sequence. The aim of this paper is to prove that in case J is finite dimensional, such a sequence is polynomially bounded if and only if the variety generated by J does not contain U J 2 , the special Jordan algebra of 2 × 2 upper triangular matrices. As an immediate consequence, we prove that U J 2 is the only finite dimensional special Jordan algebra that generates a variety of almost polynomial growth.
A proof of Carleson's $\varepsilon^2$-conjecture
2019
In this paper we provide a proof of the Carleson $\varepsilon^2$-conjecture. This result yields a characterization (up to exceptional sets of zero length) of the tangent points of a Jordan curve in terms of the finiteness of the associated Carleson $\varepsilon^2$-square function.
On the Rational Homogeneous Manifold Structure of the Similarity Orbits of Jordan Elements in Operator Algebras
1991
Considering a topological algebra B with unit e, an open group of invertible elements B −1 and continuous inversion (e. g. B = Banach algebra, B = C∞(Ω, M n (ℂ)) (Ω smooth manifold), B = special algebras of pseudo-differential operators), we are going to define the set of Jordan elements J ⊂ B (such that J = Set of Jordan operators if B = L(H), H Hilbert space) and to construct rational local cross sections for the operation mapping $$ {B^{ - 1}} \mathrel\backepsilon g \mapsto gJ{g^{ - 1}} $$ of B −1 on the similarity orbit S(J):= {gJg −1: g Є B −1}, J Є J.
Specht property for some varieties of Jordan algebras of almost polynomial growth
2019
Abstract Let F be a field of characteristic zero. In [25] it was proved that U J 2 , the Jordan algebra of 2 × 2 upper triangular matrices, can be endowed up to isomorphism with either the trivial grading or three distinct non-trivial Z 2 -gradings or by a Z 2 × Z 2 -grading. In this paper we prove that the variety of Jordan algebras generated by U J 2 endowed with any G-grading has the Specht property, i.e., every T G -ideal containing the graded identities of U J 2 is finitely based. Moreover, we prove an analogue result about the ordinary identities of A 1 , a suitable infinitely generated metabelian Jordan algebra defined in [27] .
Polynomial identities for the Jordan algebra of upper triangular matrices of order 2
2012
Abstract The associative algebras U T n ( K ) of the upper triangular matrices of order n play an important role in PI theory. Recently it was suggested that the Jordan algebra U J 2 ( K ) obtained by U T 2 ( K ) has an extremal behaviour with respect to its codimension growth. In this paper we study the polynomial identities of U J 2 ( K ) . We describe a basis of the identities of U J 2 ( K ) when the field K is infinite and of characteristic different from 2 and from 3. Moreover we give a description of all possible gradings on U J 2 ( K ) by the cyclic group Z 2 of order 2, and in each of the three gradings we find bases of the corresponding graded identities. Note that in the graded ca…
A continuous circle of pseudo-arcs filling up the annulus
1999
We prove an early announcement by Knaster on a decomposition of the plane. Then we establish an announcement by Anderson saying that the plane annulus admits a continlous decomposition into pseudo-arcs such that the quotient space is a simple closed curve. This provides a new plane curve, "a selectible circle of pseudo-aics", and answers some questions of Lewis.
Extended-order algebras as a generalization of posets
2011
Motivated by the recent study of several researchers on extended-order algebras, introduced by C. Guido and P. Toto as a possible common framework for the majority of algebraic structures used in many-valued mathematics, the paper focuses on the properties of homomorphisms of the new structures, considering extended-order algebras as a generalization of partially ordered sets. The manuscript also introduces the notion of extended-relation algebra providing a new framework for developing the theory of rough sets.
Relationships between core self-evaluation, leader empowering behavior, and job security among Jordan University Hospital nurses
2021
Nurses are facing real stressors due to patients’ needs and leaders’ demands. The aim of this study is to explore the perceived level of core self-evaluation (CSE), leader empowering behavior (LEB), and job security among Jordan University Hospital nurses in Amman, the capital of Jordan. Furthermore, it investigates the relationship between the selected variables. Differences of gender, educational level, experience, and site of work are also examined with job security. Moreover, it evaluates the contribution of CSE, LEB, gender, educational level, experience, and site of work in predicting job security among Jordan University Hospital nurses. A descriptive cross-sectional design was adopte…