Smash积，辫积和L-R Smash积的新对偶  

The New Dual of Smash Products,Braided Products and L-R Smash Products

作　　者：张良云[1] 李强[1] 

机构地区：[1]南京农业大学理学院,江苏南京210095

出　　处：《Journal of Mathematical Research and Exposition》2007年第3期577-585,共9页数学研究与评论（英文版）

基　　金：国家自然科学基金(10571153);中国科学博士后基金(2005037713).

摘　　要：本文主要地证明:由H-重模代数A,B构成的Smash积A#B的新对偶H(A#B)~0恰好是由重模余代数_HA^0,_HB^0构成的Smash余积_HA^0×_HB^0;如果(H,σ)是辫化Hopf代数,则新对偶_HH^0是右,左H^0-重模余代数;由量子Yang-Baxter H-模代数A,B构成的辫积AαB的新对偶(AαB)~0恰好是由量子Yang-Baxiter H-模余代数_HA^0,_HB^0构成的辫余积_HA^0×_HB^0.最后它给出由H-双模代数A构成的L-R Smash积A■H的新对偶(A■H)_H^0的正合序列。In this paper, we prove that the new dual H（A#B）° of the Smash product A#B introduced by dimodule algebras A and B is a Smash coproduct HA°×HB° introduced by dimodule coalgebras HA° and HB°. If （H,σ） is a braided Hopf algebra, we show that HH° is a right, left H°-dimodule coalgebra, and then prove that the new dual H（A ∝ B）° of the braided product A ∝ B introduced by quantum Yang-Baxter module algebras A and B is a braided coproduct HA°×H B° introduced by quantum Yang-Baxter module coalgebras HA° and HB°. An exact sequence of the new dual （AヰH）H° of the L-R Smash product AヰH is given.

关 键 词：重模代数 量子Yang-Baxter模代数 SMASH积 辫积 L-R SMASH积 

分 类 号：O153.5[理学—数学]