The New Dual of Smash Products, Braided Products and L-R Smash Products
Received:August 18, 2005  Revised:November 03, 2005
Key Words: dimodule algebra   quantum Yang-Baxter module algebra   Smash product   briaided product   L-R Smash product.  
Fund Project:the National Natural Science Foundation of China (10571153);
Author NameAffiliation
ZHANG Liang-yun College of Science, Nanjing Agricultural University, Jiangsu 210095, China 
LI Qiang College of Science, Nanjing Agricultural University, Jiangsu 210095, China 
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Abstract:
      In this paper, we prove that the new dual $_H(A\# B)^0$ of the Smash product $A\# B$ introduced by dimodule algebras $A$ and $B$ is a Smash coproduct $_HA^0\times _HB^0$ introduced by dimodule coalgebras $_HA^0$ and $_HB^0$. If $(H,\sigma)$ is a braided Hopf algebra, we show that $_HH^0$ is a right, left $H^0$-dimodule coalgebra, and then prove that the new dual $_H(A\propto B)^0$ of the braided product $A\propto B$ introduced by quantum Yang-Baxter module algebras $A$ and $B$ is a braided coproduct $_HA^0\times _HB^0$ introduced by quantum Yang-Baxter module coalgebras $_HA^0$ and $_HB^0$. An exact sequence of the new dual ${(A\natural H)_H}^0$ of the L-R Smash product $A\natural H$ is given.
Citation:
DOI:10.3770/j.issn:1000-341X.2007.03.017
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