弱Hopf代数上的对角交叉积和左右冲积(英文)  

Diagonal Crossed Products and L-R Smash Products Over Weak Hopf Algebras

作　　者：侯波[1] 张子龙[1] 蔡炳苓[1] 

机构地区：[1]河北师范大学数学与信息科学学院,河北石家庄050024

出　　处：《数学进展》2012年第3期320-334,共15页Advances in Mathematics（China）

基　　金：supported by NSFC(No.10971049,No.109071052);the NSF of Hebei Province(No.A2008000135,No.A2009000253)

摘　　要：作为弱Hopf代数上的冲积的推广,本文引入了弱Hopf代数上的对角交叉积和左右冲积概念,并研究了它们的性质.特别地,有限维弱Hopf代数上的Drinfeld对是一种特殊的对角交叉积,本文给出了其上的弱Hopf代数结构.作为两个典型的例子,本文引入并研究了弱Hopf代数上Kadison积和Connes-Moscovici积.The notions of the diagonal crossed product and the L-R smash product over weak Hopf algebras, which can be seen as generalizations of smash products over weak Hopf algebras, are introduced and studied. In particular, the weak Hopf algebraic structure of the Drinfeld double of a finite dimensional weak Hopf algebra, which is a special case of diagonal crossed products, is given. Moreover, two canonical examples, the Kadison products and the Connes-Moscovici products over weak Hopf algebras, are introduced and investigated.

关 键 词：对角交叉积 左右冲积 Drinfeld对 弱HOPF代数 

分 类 号：O153[理学—数学]