Braided bialgebras and quadratic blalgebras
Braided bialgebras and quadratic blalgebras
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DOI：
10.1080/00927879308824649
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发表时间：
1993
影响因子：
0.7
通讯作者：
Yukio Doi
中科院分区：
文献类型：
--
作者：
Yukio Doi
简介：辫子双代数的概念是由Larson-Towber [LT]和Hayashi [HI]独立地引入的，它是一对（A，a），其中A是交换环k上的双代数，u是A上满足三个特定条件的可逆双线性型（定义1.1）.在本文中，我们使用u而不是Larson和Towber使用的t，其中t：A@ A-+ A@ A是经典扭曲。第一节总结了辫双代数的一些基本性质。我们证明了（定理1.3）：任何辫子Hopf代数的对极都是双射的。进一步，我们从具有可逆”2-上圈”a的交换双代数构造了（定理1.6）（w-三角）辫子双代数.回想一下著名的由Yang-Baxter算子R：k”@ kn-，k”@ kn构造的FRT-结构A（R），它也是一个辫子双代数.有几种不同的方法来构造A（R），例如[TI，[LT]。第2节致力于扩展这样的FRT结构。任何
Introduction: The concept of a braided bialgebra was introduced by Larson-Towber [LT] and independently by Hayashi [HI, which is a pair (A, a) where A is a bialgebra over a commutative ring k and u is an invertible bilinear form on A satisfying three specific conditions (DEFINITION 1.1). In this paper we work with u rather than a t which Larson and Towber work with, where t: A@ A-+ A@ A is the classical twist. We summarize in Section I some basic properties on braided bialgebras. We show (THEOREM 1.3) that the antipode of any braided Hopf algebra is bijective. Further we construct (THEOREM 1.6)(w-triangular) braided bialgebras from commutative bialgebras with invertible" 2-cocycles" a.Recall the well known FRT-construction A (R) from a Yang-Baxter operator R: k"@ kn-, k"@ kn, which is also a braided bialgebra. There are several distinct ways to construct A (R), eg [TI,[LT]. Section 2 is devoted to extending such a FRT-construction. For any