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Smash积，辫积和L-R Smash积的新对偶
  • 期刊名称：数学研究与评论，27（3）:577-585，2007
  • 时间：0
  • 分类：O153.3[理学—数学;理学—基础数学]
  • 作者机构：[1]南京农业大学理学院,江苏南京210095
  • 相关基金：基金项目：国家自然科学基金（10571153）;中国科学博士后基金（2005037713）.
  • 相关项目：结合代数的Quiver刻划和Hopf代数表示型分类以及与量子群理论的联系
关键词： 重模代数, 量子Yang-Baxter模代数, SMASH积, 辫积, L-R, SMASH积, dimodule algebra, quantum Yang-Baxter module algebra, Smash product, briaided product, L-R Smash product.
中文摘要：

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）°恰好是由重模余代数HA°,HB°构成的Smash余积HA°× HB°；如果（H，σ）是辫化Hopf代数，则新对偶HH°是右，左H°-重模余代数；由量子Yang-Baxter H-模代数A，B构成的辫积A∝B的新对偶（A∝B）°恰好是由量子Yang-Baxter H-模余代数HA°，HB°构成的辫余积HA°×HB°，最后它给出由H-双模代数A构成的L-R Smash积AヰH的新对偶（AヰH）H°的正合序列。

英文摘要：

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.

同期刊论文项目
结合代数的Quiver刻划和Hopf代数表示型分类以及与量子群理论的联系
期刊论文 63 获奖 1 著作 4
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