The article explains the meaning and its extreme importance of the strategic heights for the standardization field, deliberates over the challenges for traditional standardization, and proposes the urgency of the tran...The article explains the meaning and its extreme importance of the strategic heights for the standardization field, deliberates over the challenges for traditional standardization, and proposes the urgency of the transformation towards modernized standardization. Affirming the limited role of existing methods like modularization and comprehensive standardization, the author insists on the necessity of accelerating the development of modernized standardization to meet the increasing demand of modern society towards standardization. It is a historical mission for current standardizers to focus on theories, methodologies and innovations in the modern standardization arena.展开更多
The authors consider a family of finite-dimensional Lie superalgebras of C-type over an algebraically closed field of characteristic p 〉 3. It is proved that the Lie superalgebras of C-type are simple and the spannin...The authors consider a family of finite-dimensional Lie superalgebras of C-type over an algebraically closed field of characteristic p 〉 3. It is proved that the Lie superalgebras of C-type are simple and the spanning sets are determined. Then the spanning sets are employed to characterize the superderivation algebras of these Lie superalgebras. Finally, the associative forms are discussed and a comparison is made between these Lie superalgebras and other simple Lie superalgebras of Cartan type.展开更多
For any complex parameters a and b,W(a,b)is the Lie algebra with basis{Li,Wi|i∈Z}and relations[Li,Lj]=(j i)Li+j,[Li,Wj]=(a+j+bi)Wi+j,[Wi,Wj]=0.In this paper,indecomposable modules of the intermediate series over W(a,...For any complex parameters a and b,W(a,b)is the Lie algebra with basis{Li,Wi|i∈Z}and relations[Li,Lj]=(j i)Li+j,[Li,Wj]=(a+j+bi)Wi+j,[Wi,Wj]=0.In this paper,indecomposable modules of the intermediate series over W(a,b)are classified.It is also proved that an irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight module or a uniformly bounded module.Furthermore,if a∈/Q,an irreducible weight W(a,b)-module is simply a Vir-module with trivial actions of Wk’s.展开更多
This paper investigates the structure of the"missing part"from the category of coherent sheaves over a weighted projective line of weight type(2,2,n)to the category of finitely generated right modules on the...This paper investigates the structure of the"missing part"from the category of coherent sheaves over a weighted projective line of weight type(2,2,n)to the category of finitely generated right modules on the associated canonical algebra.By constructing a t-structure in the stable category of the vector bundle category,we show that the"missing part"is equivalent to the heart of the t-structure,hence it is abelian.Moreover,it is equivalent to the category of finitely generated modules on the path algebra of type An-1.展开更多
Let G be a semisimple group over an algebraically closed field of characteristic p > 0. We give a(partly conjectural) closed formula for the character of many indecomposable tilting rational G-modules assuming that...Let G be a semisimple group over an algebraically closed field of characteristic p > 0. We give a(partly conjectural) closed formula for the character of many indecomposable tilting rational G-modules assuming that p is large.展开更多
We propose the notion of Hopf module algebra and show that the projection onto the subspace of coinvariants is an idempotent Rota-Baxter operator of weight-1. We also provide a construction of Hopf module algebras by ...We propose the notion of Hopf module algebra and show that the projection onto the subspace of coinvariants is an idempotent Rota-Baxter operator of weight-1. We also provide a construction of Hopf module algebras by using Yetter-Drinfeld module algebras. As an application,we prove that the positive part of a quantum group admits idempotent Rota-Baxter algebra structures.展开更多
We conjecture an explicit bound on the prime characteristic of a field, under which the Weyl modules of affine sl_2 and the minimal series modules of Virasoro algebra remain irreducible, and Goddard-Kent-Olive coset c...We conjecture an explicit bound on the prime characteristic of a field, under which the Weyl modules of affine sl_2 and the minimal series modules of Virasoro algebra remain irreducible, and Goddard-Kent-Olive coset construction for affine sl_2 is valid.展开更多
Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A#σH are coincident. This is...Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A#σH are coincident. This is an improvement of the conclusion about representation type of an algebra in Li and Zhang [Sci China Ser A, 2006, 50: 1-13]. Secondly, we give the relationship between Gorenstein projective modules over A and that over A#σH. Then, using this result, it is proven that A is a finite dimensional CM-finite Gorenstein algebra if and only if so is A#σH.展开更多
This paper proves that the restriction of a Specht module for a(degenerate or non-degenerate)cyclotomic Hecke algebra, or KLR(Khovanov-Lauda-Rouquier) algebra, of type A has a Specht filtration.
Let F be an algebraically closed field of prime characteristic p>3,and W(n)the Witt superalgebra over F,which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates.The dimensions ...Let F be an algebraically closed field of prime characteristic p>3,and W(n)the Witt superalgebra over F,which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates.The dimensions of simple atypical modules in the restricted supermodule category for W(n)are precisely calculated in this paper,and thereby the dimensions of all simple modules can be precisely given.Moreover,the restricted supermodule category for W(n)is proved to have one block.展开更多
文摘The article explains the meaning and its extreme importance of the strategic heights for the standardization field, deliberates over the challenges for traditional standardization, and proposes the urgency of the transformation towards modernized standardization. Affirming the limited role of existing methods like modularization and comprehensive standardization, the author insists on the necessity of accelerating the development of modernized standardization to meet the increasing demand of modern society towards standardization. It is a historical mission for current standardizers to focus on theories, methodologies and innovations in the modern standardization arena.
基金supported by the National Natural Science Foundation of China(No.11371182)the PhD Start-up Foundation of Liaoning University of China(No.2012002)the Predeclaration Fund of State Project of Liaoning University(No.2014LDGY01)
文摘The authors consider a family of finite-dimensional Lie superalgebras of C-type over an algebraically closed field of characteristic p 〉 3. It is proved that the Lie superalgebras of C-type are simple and the spanning sets are determined. Then the spanning sets are employed to characterize the superderivation algebras of these Lie superalgebras. Finally, the associative forms are discussed and a comparison is made between these Lie superalgebras and other simple Lie superalgebras of Cartan type.
基金supported by National Natural Science Foundation of China(Grant Nos.11371287,11301130,11001200 and 11101269)the Fundamental Research Funds for the Central Universities Shanghai Municipal Science and Technology Commission(Grant No.12XD1405000)
文摘For any complex parameters a and b,W(a,b)is the Lie algebra with basis{Li,Wi|i∈Z}and relations[Li,Lj]=(j i)Li+j,[Li,Wj]=(a+j+bi)Wi+j,[Wi,Wj]=0.In this paper,indecomposable modules of the intermediate series over W(a,b)are classified.It is also proved that an irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight module or a uniformly bounded module.Furthermore,if a∈/Q,an irreducible weight W(a,b)-module is simply a Vir-module with trivial actions of Wk’s.
基金supported by National Natural Science Foundation of China(Grant Nos.11201386,10931006,11071040 and 11201388)the Natural Science Foundation of Fujian Province of China(Grant No.2012J05009)
文摘This paper investigates the structure of the"missing part"from the category of coherent sheaves over a weighted projective line of weight type(2,2,n)to the category of finitely generated right modules on the associated canonical algebra.By constructing a t-structure in the stable category of the vector bundle category,we show that the"missing part"is equivalent to the heart of the t-structure,hence it is abelian.Moreover,it is equivalent to the category of finitely generated modules on the path algebra of type An-1.
基金G.Lusztig was supported by National Science Foundation of USA(GrantNo.DMS-1303060)by a Simons Fellowship
文摘Let G be a semisimple group over an algebraically closed field of characteristic p > 0. We give a(partly conjectural) closed formula for the character of many indecomposable tilting rational G-modules assuming that p is large.
基金supported by National Natural Science Foundation of China(Grant No.11201067)the Matching Fund for National Natural Science Foundation of China from Dongguan University of Technology(Grant No.ZF121006)
文摘We propose the notion of Hopf module algebra and show that the projection onto the subspace of coinvariants is an idempotent Rota-Baxter operator of weight-1. We also provide a construction of Hopf module algebras by using Yetter-Drinfeld module algebras. As an application,we prove that the positive part of a quantum group admits idempotent Rota-Baxter algebra structures.
基金supported by the National Science Foundation of USA(Grant No. DMS1405131)
文摘We conjecture an explicit bound on the prime characteristic of a field, under which the Weyl modules of affine sl_2 and the minimal series modules of Virasoro algebra remain irreducible, and Goddard-Kent-Olive coset construction for affine sl_2 is valid.
基金supported by National Natural Science Foundation of China (Grant No.11171296)the Zhejiang Provincial Natural Science Foundation of China (Grant No. D7080064)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110101110010)
文摘Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A#σH are coincident. This is an improvement of the conclusion about representation type of an algebra in Li and Zhang [Sci China Ser A, 2006, 50: 1-13]. Secondly, we give the relationship between Gorenstein projective modules over A and that over A#σH. Then, using this result, it is proven that A is a finite dimensional CM-finite Gorenstein algebra if and only if so is A#σH.
文摘This paper proves that the restriction of a Specht module for a(degenerate or non-degenerate)cyclotomic Hecke algebra, or KLR(Khovanov-Lauda-Rouquier) algebra, of type A has a Specht filtration.
基金supported by the National Natural Science Foundation of China(Nos.11126062,11201293,11226327,11271130)the Innovation Program of Shanghai Municipal Education Commission(Nos.12ZZ038,13YZ077)
文摘Let F be an algebraically closed field of prime characteristic p>3,and W(n)the Witt superalgebra over F,which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates.The dimensions of simple atypical modules in the restricted supermodule category for W(n)are precisely calculated in this paper,and thereby the dimensions of all simple modules can be precisely given.Moreover,the restricted supermodule category for W(n)is proved to have one block.