双代数的一种实现方法及与某些实现相关的Hopf代数
A method of realization of bialgebras, and Hopf algebras associated to some realizations
摘要：
本文介绍了一种方法，它从简单而相当一般的数学数据出发，允许构造算子的线性代数，每个算子都被赋予一个双代数结构（余积和公共性）。在一定的条件下，我们得到了算子的线性代数，它们要么是一个Hopf代数，要么是它的双代数结构决定了一个更抽象的相伴Hopf代数，最后给出了这些双代数存在唯一相伴Hopf代数的一个更一般的抽象条件.介绍是适应的情况下，线性算子的代数不是非线性生成的。本文仅限于阐述的方法建设和证明的存在性和唯一性的结构与每个代数的线性算子的建设。然而，可以注意到，与所获得的双代数相关联的关系的理想确定了理论上感兴趣的代数域。
英文摘要：
This article introduces a method, which starting from simple and quite general mathematical data, allows to construct linear algebras of operators which are, each of them, endowed with a bialgebra structure (coproduct and counity). Moreover under some explicit and natural conditions on theses mathematical data we obtain linear algebras of operators with the following property: each of them, is either a Hopf algebra, or its bialgebra structure determines a more abstract Hopf algebra associated with it. Finally, we describe a more general abstract condition for theses bialgebras to admit a unique associated Hopf algebra. The presentation is adapted to the cases where the algebras of linear operators are not finitely generated. This article is restricted to the exposition of the method of construction and to the proofs of existence and uniqueness of the structures associated with each algebra of linear operators that are constructed. Nevertheless, it may be noticed that the ideals of relations associated with bialgebras that are obtained determine an algebraic domain which is of theoretical interest .
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