In this paper, we first give a sufficient and necessary condition for a Hopf algebra to be a Yetter-Drinfel'd module, and prove that the finite dual of a Yetter-Drinfel'd module is still a Yetter-Drinfel'd...In this paper, we first give a sufficient and necessary condition for a Hopf algebra to be a Yetter-Drinfel'd module, and prove that the finite dual of a Yetter-Drinfel'd module is still a Yetter-Drinfel'd module. Finally, we introduce a concept of convolution module.展开更多
This paper is devoted to studying the structures of the cell modules of the complexified Green algebra R(D(H_(4))),where D(H_(4))is the Drinfel'd quantum double of Sweedler's 4-dimensional Hopf algebra H_(4).W...This paper is devoted to studying the structures of the cell modules of the complexified Green algebra R(D(H_(4))),where D(H_(4))is the Drinfel'd quantum double of Sweedler's 4-dimensional Hopf algebra H_(4).We show that R(D(H_(4)))has one infinite dimensional cell module,one 4-dimensional cell module generated by all finite dimensional indecomposable projective modules of D(H_(4))and infinitely many 2-dimensional cell modules.More precisely,we obtain the decompositions of all finite dimensional cell modules into the direct sum of indecomposable submodules,and show that the infinite dimensional cell module can be written as the direct sum of two infinite dimensional indecomposable submodules.展开更多
Variable separation approach that is based on Baeicklund transformation （BT-VSA） is extended to solve the （3＋1）-dimensional Jimbo- Miwa equation and the （1＋1）-dimensional Drinfel＇d-Sokolov Wilson equation. Ne...Variable separation approach that is based on Baeicklund transformation （BT-VSA） is extended to solve the （3＋1）-dimensional Jimbo- Miwa equation and the （1＋1）-dimensional Drinfel＇d-Sokolov Wilson equation. New exact solutions, which include some low-dimensional functions, are obtained. One of the low-dimensional function is arbitrary and another must satisfy a Riccati equation. Some new localized excitations can be derived from （2＋1）-dimensional localized excitations and for simplification, we omit those in this letter.展开更多
IN zoology, the developmental stage of individual from zygote to hatching was called embryo. The modem embryology is a branch of study on the organism’ s embryos. The palaeoembryology is a new field in palaeontology,...IN zoology, the developmental stage of individual from zygote to hatching was called embryo. The modem embryology is a branch of study on the organism’ s embryos. The palaeoembryology is a new field in palaeontology, and it has not been considered an important field before, because the invertebrate’s eggs or embryos are minute size and without mineralized envelope. Until now, fossilized eggs of invertebrates in Cambrian have been rarely reported and most of them are small globular structures without recognizable features. Other reported fossilized embryos found from Middle Cambrian are spherical with a展开更多
文摘In this paper, we first give a sufficient and necessary condition for a Hopf algebra to be a Yetter-Drinfel'd module, and prove that the finite dual of a Yetter-Drinfel'd module is still a Yetter-Drinfel'd module. Finally, we introduce a concept of convolution module.
基金Supported by Natural National Science Foundation of China(Grant Nos.12071412,11871063)。
文摘This paper is devoted to studying the structures of the cell modules of the complexified Green algebra R(D(H_(4))),where D(H_(4))is the Drinfel'd quantum double of Sweedler's 4-dimensional Hopf algebra H_(4).We show that R(D(H_(4)))has one infinite dimensional cell module,one 4-dimensional cell module generated by all finite dimensional indecomposable projective modules of D(H_(4))and infinitely many 2-dimensional cell modules.More precisely,we obtain the decompositions of all finite dimensional cell modules into the direct sum of indecomposable submodules,and show that the infinite dimensional cell module can be written as the direct sum of two infinite dimensional indecomposable submodules.
基金The author is very gruteful to referees for all kinds of help.
文摘Variable separation approach that is based on Baeicklund transformation （BT-VSA） is extended to solve the （3＋1）-dimensional Jimbo- Miwa equation and the （1＋1）-dimensional Drinfel＇d-Sokolov Wilson equation. New exact solutions, which include some low-dimensional functions, are obtained. One of the low-dimensional function is arbitrary and another must satisfy a Riccati equation. Some new localized excitations can be derived from （2＋1）-dimensional localized excitations and for simplification, we omit those in this letter.
文摘IN zoology, the developmental stage of individual from zygote to hatching was called embryo. The modem embryology is a branch of study on the organism’ s embryos. The palaeoembryology is a new field in palaeontology, and it has not been considered an important field before, because the invertebrate’s eggs or embryos are minute size and without mineralized envelope. Until now, fossilized eggs of invertebrates in Cambrian have been rarely reported and most of them are small globular structures without recognizable features. Other reported fossilized embryos found from Middle Cambrian are spherical with a
