Duality And Quantion Of Twisted Dimodule Algebras

This paper mainly studies duality and quantization of twisted dimodule algebras. First, we give the duality of twisted dimodule algebras-twisted dimodule coalgebras, and discuss Smash coproduct on it; Second, we study quantization of twisted dimodule algebras over strongly Long bialgebras; At last we give relation between Long bialgebras、Long skew bialgebras and twisted dimodule algebras.The paper is organized as follows:In chapter1, we introduce the development of twisted theories and dimodule, then we also introduce the background of study and main results in this paper.In chapter2, we give the definition of twisted dimodule coalgebras,also study Smash coproduct over it.In chapter3, we give the concept of strongly Long bialgebras,also study the quantization of twisted dimodule algebras and Smash product over it, at last give the relation between Long bialgebras、Long skew bialgebras and twisted dimodule algebras.