We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra.Sufficient and necessary conditions for the simplicity of these modules are given.From these modules we c...We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra.Sufficient and necessary conditions for the simplicity of these modules are given.From these modules we construct modules which are infinitely generated when restricted to the maximal toral subalgebra.展开更多
Perovskite solar cells(PSCs)have attracted worldwide attention due to their high efficiency and low manufacturing cost.As the largest supplier of photovoltaic modules,China has made huge endeavors in the research on P...Perovskite solar cells(PSCs)have attracted worldwide attention due to their high efficiency and low manufacturing cost.As the largest supplier of photovoltaic modules,China has made huge endeavors in the research on PSCs.In 2019,Chinese research groups were still holding the top position for paper publications in the world.Both the efficiency and the stability of the device have been steadily increasing,pushing forward the commercialization of PSCs step by step.This review summarizes the highlights of China’s PSC research progress in 2019 and briefly introduces the development of PSC modules in industry.展开更多
In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to character...In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to characterize the primary radical of a finitely generated submodule of a free module.展开更多
First, the authors give a GrSbner-Shirshov basis of the finite-dimensional irre- ducible module Vq（λ） of the Drinfeld-Jimbo quantum group Uq（G2） by using the double free module method and the known GrSbner-Shirsh...First, the authors give a GrSbner-Shirshov basis of the finite-dimensional irre- ducible module Vq（λ） of the Drinfeld-Jimbo quantum group Uq（G2） by using the double free module method and the known GrSbner-Shirshov basis of Uq（G2）. Then, by specializing a suitable version of Uq （G2） at q = 1, they get a GrSbner-Shirshov basis of the universal enveloping algebra U（G2） of the simple Lie algebra of type G2 and the finite-dimensional irreducible U（G2）-module V（λ）.展开更多
Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of int...Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras.展开更多
基金supported by NSF of China(11801117,11971315)the Natural Science Foundation of Guangdong Province,China(2018A030313268)partially supported by NSFof China(11801390).
文摘We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra.Sufficient and necessary conditions for the simplicity of these modules are given.From these modules we construct modules which are infinitely generated when restricted to the maximal toral subalgebra.
基金supported by the National Natural Science Foundation of China(11834011,11674219)。
文摘Perovskite solar cells(PSCs)have attracted worldwide attention due to their high efficiency and low manufacturing cost.As the largest supplier of photovoltaic modules,China has made huge endeavors in the research on PSCs.In 2019,Chinese research groups were still holding the top position for paper publications in the world.Both the efficiency and the stability of the device have been steadily increasing,pushing forward the commercialization of PSCs step by step.This review summarizes the highlights of China’s PSC research progress in 2019 and briefly introduces the development of PSC modules in industry.
文摘In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to characterize the primary radical of a finitely generated submodule of a free module.
基金supported by the National Natural Science Foundation of China(Nos.11061033,11361056)
文摘First, the authors give a GrSbner-Shirshov basis of the finite-dimensional irre- ducible module Vq（λ） of the Drinfeld-Jimbo quantum group Uq（G2） by using the double free module method and the known GrSbner-Shirshov basis of Uq（G2）. Then, by specializing a suitable version of Uq （G2） at q = 1, they get a GrSbner-Shirshov basis of the universal enveloping algebra U（G2） of the simple Lie algebra of type G2 and the finite-dimensional irreducible U（G2）-module V（λ）.
基金supported by Natural Sciences and Engineering Research Council of Canada (Grant No. 227060-04)Yuri Bahturin, National Science Foundation (Grant No. DMS-0700811)Russian Fund for Basic Research (Grant No. 08-01-00573)
文摘Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras.
基金This research was supported by the National Natural Science Foundation of China(10771095)the Guangxi Science Foundation(0832107,0640070)the Scientific Research Foundation of Guangxi Education Committee(200707LX233)
