After defining Hom(chi (A), eta (B)) and chi (A) circle times eta (B) in the fuzzy modular category Fm, the sufficient conditions of the existence for exact Hom functors Hom(delta (M),), and Hom(, delta (M)), as well ...After defining Hom(chi (A), eta (B)) and chi (A) circle times eta (B) in the fuzzy modular category Fm, the sufficient conditions of the existence for exact Hom functors Hom(delta (M),), and Hom(, delta (M)), as well as exact Tensor functors delta (M)circle times and circle times delta (M) are given in this paper. Finally the weak isomorphisms relations between Horn functors and Tensor functors are displayed.展开更多
In this paper we give a categorification of the n-th tensor products of the spin modules of enveloping algebra of lie algebra of type D4 via some subcategories and projective functors of the BGG category of the genera...In this paper we give a categorification of the n-th tensor products of the spin modules of enveloping algebra of lie algebra of type D4 via some subcategories and projective functors of the BGG category of the general linear Lie algebra gln over the complex field C.展开更多
The concept of （f, σ）-pair （B, H）is introduced, where B and H are Hopf algebras. A braided tensor category which is a tensor subcategory of the category ^HM of left H-comodules through an （f, σ）-pair is constr...The concept of （f, σ）-pair （B, H）is introduced, where B and H are Hopf algebras. A braided tensor category which is a tensor subcategory of the category ^HM of left H-comodules through an （f, σ）-pair is constructed. In particularly, a Yang-Baxter equation is got. A Hopf algebra is constructed as well in the Yetter-Drinfel＇d category H^HYD by twisting the multiplication of B.展开更多
Let k be the algebraic closure of a finite field $\mathbb{F}_q $ and A be a finite dimensional k-algebra with a Frobenius morphism F. In the present paper we establish a relation between the stable module category of ...Let k be the algebraic closure of a finite field $\mathbb{F}_q $ and A be a finite dimensional k-algebra with a Frobenius morphism F. In the present paper we establish a relation between the stable module category of the repetitive algebra ? of A and that of the repetitive algebra of the fixed-point algebra A F. As an application, it is shown that the derived category of A F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.展开更多
This paper is devoted to studying the recollement of the categories of finitely generated modules over finite dimensional algebras. We prove that for algebras A, B and C, if A-mod admits a recollement relative to B-mo...This paper is devoted to studying the recollement of the categories of finitely generated modules over finite dimensional algebras. We prove that for algebras A, B and C, if A-mod admits a recollement relative to B-mod and C-mod, then A[R]-mod admits a recollement relative to B[S]-mod and C-mod, where A[R]and B[S]are the one-point extensions of A by R and of B by S.展开更多
We find a new representation of the simple Lie algebra of type E6 on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this r...We find a new representation of the simple Lie algebra of type E6 on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this representation and Shen＇s idea of mixed product, we construct a new functor from Ds-Mod to E6-Mod. A condition for the functor to map a finite-dimensional irreducible Ds-module to an infinite-dimensional irreducible E6-module is obtained. Our results yield explicit constructions of certain infinite-dimensional irreducible weight E6-modules with finite-dimensional weight subspaces. In our approach, the idea of Kostant＇s characteristic identities plays a key role.展开更多
This paper gives a complete classification of (Δ)-finite twisted double incidence algebras of posets in the case where the Hasse quivers of posets are of type An.
文摘After defining Hom(chi (A), eta (B)) and chi (A) circle times eta (B) in the fuzzy modular category Fm, the sufficient conditions of the existence for exact Hom functors Hom(delta (M),), and Hom(, delta (M)), as well as exact Tensor functors delta (M)circle times and circle times delta (M) are given in this paper. Finally the weak isomorphisms relations between Horn functors and Tensor functors are displayed.
基金Supported by National Natural Science Foundation of China(Grant No.11271043)Natural Science Foundation of Beijing(Grant No.1122006)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.201111103110011)
文摘In this paper we give a categorification of the n-th tensor products of the spin modules of enveloping algebra of lie algebra of type D4 via some subcategories and projective functors of the BGG category of the general linear Lie algebra gln over the complex field C.
基金Supported by the Zhejiang Provincial Natural Science Foundation (Y607075)
文摘The concept of （f, σ）-pair （B, H）is introduced, where B and H are Hopf algebras. A braided tensor category which is a tensor subcategory of the category ^HM of left H-comodules through an （f, σ）-pair is constructed. In particularly, a Yang-Baxter equation is got. A Hopf algebra is constructed as well in the Yetter-Drinfel＇d category H^HYD by twisting the multiplication of B.
基金the National Natural Science Foundation of China (Grant No.10671016)the 985 Project of Beijing Normal University
文摘Let k be the algebraic closure of a finite field $\mathbb{F}_q $ and A be a finite dimensional k-algebra with a Frobenius morphism F. In the present paper we establish a relation between the stable module category of the repetitive algebra ? of A and that of the repetitive algebra of the fixed-point algebra A F. As an application, it is shown that the derived category of A F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.
基金the National Natural Science Foundation of China (Grant No. 10671161)
文摘This paper is devoted to studying the recollement of the categories of finitely generated modules over finite dimensional algebras. We prove that for algebras A, B and C, if A-mod admits a recollement relative to B-mod and C-mod, then A[R]-mod admits a recollement relative to B[S]-mod and C-mod, where A[R]and B[S]are the one-point extensions of A by R and of B by S.
基金Supported by NSFC(Grant Nos.11171324 and 11321101)
文摘We find a new representation of the simple Lie algebra of type E6 on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this representation and Shen＇s idea of mixed product, we construct a new functor from Ds-Mod to E6-Mod. A condition for the functor to map a finite-dimensional irreducible Ds-module to an infinite-dimensional irreducible E6-module is obtained. Our results yield explicit constructions of certain infinite-dimensional irreducible weight E6-modules with finite-dimensional weight subspaces. In our approach, the idea of Kostant＇s characteristic identities plays a key role.
文摘This paper gives a complete classification of (Δ)-finite twisted double incidence algebras of posets in the case where the Hasse quivers of posets are of type An.
