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Skew Pairs of Idempotents in Transformation Semigroups

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1705-1714页

作者： T.S.BLYTH M.H.ALMEIDA SANTOS Mathematical Institute University of St Andrews departamentode matemática F.C.T.Universidade Nova de Lisboa

An ordered pair （e, f） of idempotents of a regular semigroup is called a skew pair if ef is not idempotent whereas fe is idempotent. We have shown previously that there are four distinct types of skew pairs of idemp... 详细信息

关键词： full transformation semigroups idempotents skew pairs

On Banach Spaces Whose Unit Sphere Determines Polynomials

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Acta Mathematica Sinica,English Series 2007年第1期23卷 175-188页

作者： Jesús FERRER departamentode Análisis matemático Universidad de ValenciaDr.Moliner5046100 Burjasot(Valencia)

In this paper we study the problem of characterizing the real Banach spaces whose unit sphere determines polynomials, i.e., if two polynomials coincide in the unit sphere, is this sufficient to guarantee that they are identical？ We show that, in the frame of spaces with unconditional basis, non- reflexivity is a sufficient, although not necessary, condition for the above question to have an affirmative answer. We prove that the only lp^n spaces having this property are those with p irrational, while the only lp spaces which do not enjoy it are those with p an even integer. We also introduce a class of polynomial determining sets in any real Banach space.

关键词： unconditional basis polynomial determining property lp spaces

Jacobi Structures on Affine Bundles

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Acta Mathematica Sinica,English Series 2007年第5期23卷 769-788页

作者： J.GRABOWSKI D.IGLESIAS J.C.MARRERO E.PADRN P.URBA■SKI Mathematical InstitutePolish Academy of Sciences Sniadeckich 8P.O.Box 2100-956 WarsawPoland Instituto de matemáticas y Física FundamentalConsejo Superior de Investigaciones CientificasSerrano 12328006 MadridSpain departamentode matemática FundamentalFacultad de matemáticasUniversidad de la LagunaLa LagunaTenerifeCanary IslandsSpain Division of Mathematical Methods in PhysicsUniversity of Warsaw Hoia 7400-682 WarsawPoland

Abstract We study affine Jacobi structures （brackets） on an affine bundle π ： A → M, i.e. Jacobi brackets that close on affine functions. We prove that if the rank of A is non-zero, there is a one-toone correspondence between affine Jacobi structures on A and Lie algebroid structures on the vector bundle A^＋ = ∪p∈M Aff（Ap, R） of affine functionals. In the case rank A = 0, it is shown that there is a one-to-one correspondence between affine Jacobi structures on A and local Lie algebras on A^＋. Some examples and applications, also for the linear case, are discussed. For a special type of affine Jacobi structures which are canonically exhibited （strongly-affine or affine-homogeneous Jacobi structures） over a real vector space of finite dimension, we describe the leaves of its characteristic foliation as the orbits of an affine representation. These affine Jacobi structures can be viewed as an analog of the Kostant-Arnold-Liouville linear Poisson structure on the dual space of a real finite-dimensional Lie algebra.

关键词： Vector and affine bundles Jacobi manifolds Lie algebroids

Fountain-Gould Left Orders for Associative Pairs

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Acta Mathematica Sinica,English Series 2006年第3期22卷 641-652页

作者： José A.ANQUELA Teresa CORTS Miguel GóMEZ LOZANO Mercedes SILES MOLINA Departamento de matemáticas Universidad de Oviedo departamentode lgebra Geometríay TopologíaFacultad de CienciasUniversidad de MálagaCampus de Teatinos29071 MálagaSpain

In this paper, we introduce a notion of weak Fountain-Gould left order for associative pairs and give a Goldie-like theory of associative pairs which are weak Fountain Gould left orders in semiprime pairs coinciding w... 详细信息

关键词： Fountain-Gould left order Associtive pair Goldie theory