The struction of s - affine weyl groups of finite dimension simple lie algebra 素特征域上扭仿射李代数的实现
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Weyl ' s theorem 魏尔定理
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The weyl - moyal transformation takes operator multiplication into the moyal product of functions on the phase space 希尔伯特空间算子乘积与量子空间的函数moyal星乘积之间的关系是由weyl - moyal变换联系起来的。
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Hermann weyl " , , " in these days the angel of topology and the devil of abstract algebra fight for the soul of each individual matehmatical domain . " , 在这些日子里,拓扑这个天使和抽象代数这个魔鬼为各自占有每一块数学领域而斗争著.
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The paper is organized as follows . in the first section , we introduce some backgrounds and recall the definitions including weyl type algebra , smash product and ore extension 本文具体组织如下：第一节主要介绍了基本概念和理论背景，给出了weyl型代数， smash积，和ore扩张等基本概念。
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We present the definition of schubert submodules and what m . e . hall has done . chapter 2 is preliminaries . we cite some relevant lemmas to introduce the properties of w , which is an element in weyl group of a lie algebra 第二节是概念和背景知识，主要是给出一些本文用到的概念及符号，以及一些本文用到的与w的性质相关的引理；并着重介绍引理2
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Hermann weyl " , , " without the concepts , methods and results found and developed by previous generations right down to greek antiquity one cannot understand either the aims or the achievements of mathematics in the last fifty years . " , 如果不知道远溯古希腊各代前辈所建立和发展的概念,方法和结果,我们就不可能理解近五十年来数学的目标,也不可能理解它的成就.
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In this paper , the folio wings are introduced briefly : holonomic theory ; the basic idea that d . zeilberger used to prove identities using holonomic theory . and wu method is generalized to the non - commutative weyl algebra . furthermore , dialytic method of elimination is replaced by wu method , so the prove can be extended from the single - variable hypergeometric identities to multi - variable ones 本文简要介绍了完整性理论， d . zeilberger利用完整性理论证明恒等式的基本思想，将吴方法推广到不可交换的weyl代数上，用吴方法取代了d . zeilberg在证明完整性函数恒等式的理论框架中的析配消元法，从而将这种证明理论由单变量超几何恒等式的证明扩展到多变量超几何恒等式的证明。
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Let d be a nonzero k - vector space of commuting - derivations of a . kaim - ing zhao and yucai su studied the associative algebra a [ d ] = ak [ d ] of weyl type constructed from the pair of a commutative associative algebra . 4 and its commutative derivation subalgebra d over a field k of arbitrary characteristic 赵开明和苏育才研究了任意特征的域上具有单位元的交换结合代数a和它的交换导子的子空间d所构造的weyl型代数。他们证明了a [ d ]是单lie代数的充分必要条件是a是d -单的且k _ 1 [ d ]忠实地作用在a上。
