Y. Doi has investigated the H-comodule algebra since 1983. The structure theorem of cleft H-comodule algebra was given by Y. Doi and M. Takeuchi in 1986, i. e. if A is a cleft H-comodule algebra then A≌A<sub>0&...Y. Doi has investigated the H-comodule algebra since 1983. The structure theorem of cleft H-comodule algebra was given by Y. Doi and M. Takeuchi in 1986, i. e. if A is a cleft H-comodule algebra then A≌A<sub>0</sub>#<sub>σ</sub>H as algebra. The dual notion of H-comodule algebra is H-module coalgebra. Y. Doi also studied the H-module coalgebra. However, he did not obtain the structure theorem of cocleft H-module coalgebra. In this note we introduce crossed coproducts which are the dual notion展开更多
In this paper, we introduce the concept of a group twisted tensor biproduct and give the necessary and sufficient conditions for the new object to be a Hopf group coalgebra.
In this paper, we construct a cocylindrical object associated to two coalgebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduet coalgebra induced ...In this paper, we construct a cocylindrical object associated to two coalgebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduet coalgebra induced from two coalgebras with a cotwisted map and the cocyclic object related to the diagonal of the cocylindrical object.展开更多
In this paper,the correspondence theorem for the usual algebraic systems is generalized to coalgebra.Moreover,one example,which illustrate the preimage of a subcoalgebra need not to be a subcoalgebra for general coalg...In this paper,the correspondence theorem for the usual algebraic systems is generalized to coalgebra.Moreover,one example,which illustrate the preimage of a subcoalgebra need not to be a subcoalgebra for general coalgebra homomorphism,is given.展开更多
In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is ...In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is to prove a structure theorem about B cocleft H module coalgebras.展开更多
In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is ...In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is a generalization of the decompostion theorem of coalgebra.展开更多
In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple grap...In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.展开更多
文摘Y. Doi has investigated the H-comodule algebra since 1983. The structure theorem of cleft H-comodule algebra was given by Y. Doi and M. Takeuchi in 1986, i. e. if A is a cleft H-comodule algebra then A≌A<sub>0</sub>#<sub>σ</sub>H as algebra. The dual notion of H-comodule algebra is H-module coalgebra. Y. Doi also studied the H-module coalgebra. However, he did not obtain the structure theorem of cocleft H-module coalgebra. In this note we introduce crossed coproducts which are the dual notion
基金Supported by the National Natural Science Foundation of China（10871170） Supported by the Educational Minister Science Technology Key Foundation of China（108154）
文摘这份报纸，主要由一种新方法为模块 coalgebras 给结构定理，并且删除 Hopf 代数学 H 的相对极 S 是 bijective 的条件。
基金Supported by the Fund of the Key Disciplines of Xinjiang Uygur Autonomous Region(2012ZDXK03)
文摘In this paper, we introduce the concept of a group twisted tensor biproduct and give the necessary and sufficient conditions for the new object to be a Hopf group coalgebra.
基金The NSF(11261063,11171183)of Chinathe Fund(2012ZDXK03)of the Key Disciplines in the General Colleges and Universities of Xinjiang Uygur Autonomous Region+1 种基金the Foundation(2013721043)for Excellent Youth Science and Technology Innovation Talents of Xinjiang Uygur Autonomous Regionthe NSF(ZR2011AM013)of Shandong Province
文摘In this paper, we construct a cocylindrical object associated to two coalgebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduet coalgebra induced from two coalgebras with a cotwisted map and the cocyclic object related to the diagonal of the cocylindrical object.
文摘In this paper,the correspondence theorem for the usual algebraic systems is generalized to coalgebra.Moreover,one example,which illustrate the preimage of a subcoalgebra need not to be a subcoalgebra for general coalgebra homomorphism,is given.
文摘In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is to prove a structure theorem about B cocleft H module coalgebras.
文摘In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is a generalization of the decompostion theorem of coalgebra.
文摘In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.
