We show that the torsion module Tor_(j)^(R)(R/a,H_(a)^(i)(X))is in a Serre subcategory for the bounded below R-complex X.In addition,we prove the isomorphism Tor_(s-t)^(R)(R/a,X)≅Tor_(s)^(R)(R/a,H_(a)^(t)(X))in some c...We show that the torsion module Tor_(j)^(R)(R/a,H_(a)^(i)(X))is in a Serre subcategory for the bounded below R-complex X.In addition,we prove the isomorphism Tor_(s-t)^(R)(R/a,X)≅Tor_(s)^(R)(R/a,H_(a)^(t)(X))in some case.As an application,the Betti number of a complex X in a prime ideal p can be computed by the Betti number of the local cohomology modules of X in p.展开更多
The aim of this paper is to categorify the n-th tensor power of the vector representation of U（ ο（7,C））. The main tools are certain singular blocks and projective functors of the BGG category of the complex Lie a...The aim of this paper is to categorify the n-th tensor power of the vector representation of U（ ο（7,C））. The main tools are certain singular blocks and projective functors of the BGG category of the complex Lie algebra gln.展开更多
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
We prove that, confined that G > H > P and P is a proper p-subgroup of H, if H ∩~gH ≤ P for any g ∈ G-H, then the operator of the restriction to RH of RG-modules induces a triangulated equivalence from StmodP...We prove that, confined that G > H > P and P is a proper p-subgroup of H, if H ∩~gH ≤ P for any g ∈ G-H, then the operator of the restriction to RH of RG-modules induces a triangulated equivalence from StmodP(RG) to StmodP(RH); if the normal subgroup H controls the fusion of p-subgroups of G, the restriction functor is a faithful triangulated functor; if P is strongly closed in H respect to G, the same functor is also a faithful triangulated functor.展开更多
Through discussing the transformation of the invariant ideals, we firstly prove that the T-functor can only decrease the embedding dimension in the category of unstable algebras over the Steenrod algebra. As a corolla...Through discussing the transformation of the invariant ideals, we firstly prove that the T-functor can only decrease the embedding dimension in the category of unstable algebras over the Steenrod algebra. As a corollary we obtain that the T-functor preserves the hypersurfaces in the category of unstable algebras. Then with the applications of these results to invariant theory, we provide an alternative proof that if the invariant of a finite group is a hypersurface, then so are its stabilizer subgroups. Moreover, by several counter-examples we demonstrate that if the invariants of the stabilizer subgroups or Sylow p-subgroups are hypersurfaces, the invariant of the group itself is not necessarily a hypersurface.展开更多
基金Natural Science Foundation of Gansu Province(23JRRA866)Higher Education Innovation Fund of Gansu Provincial Department of Education(2025A-132)+1 种基金University-level Scientific Research and Innovation Project of Gansu University of Political Science and Law(GZF2024XQN16)Youth Foundation of Lanzhou Jiaotong University(2023023)。
文摘We show that the torsion module Tor_(j)^(R)(R/a,H_(a)^(i)(X))is in a Serre subcategory for the bounded below R-complex X.In addition,we prove the isomorphism Tor_(s-t)^(R)(R/a,X)≅Tor_(s)^(R)(R/a,H_(a)^(t)(X))in some case.As an application,the Betti number of a complex X in a prime ideal p can be computed by the Betti number of the local cohomology modules of X in p.
基金Supported by the Natural Science Foundation of Beijing(Grant No.1122006)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.201111103110011)Science and Technology Foundation of BJUT(Grant No.ykj-4787)
文摘The aim of this paper is to categorify the n-th tensor power of the vector representation of U（ ο（7,C））. The main tools are certain singular blocks and projective functors of the BGG category of the complex Lie algebra gln.
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 the National Natural Science Foundation of China(10826057)
文摘We prove that, confined that G > H > P and P is a proper p-subgroup of H, if H ∩~gH ≤ P for any g ∈ G-H, then the operator of the restriction to RH of RG-modules induces a triangulated equivalence from StmodP(RG) to StmodP(RH); if the normal subgroup H controls the fusion of p-subgroups of G, the restriction functor is a faithful triangulated functor; if P is strongly closed in H respect to G, the same functor is also a faithful triangulated functor.
基金Supported by the National Natural Science Foundation of China(Grant No.11371343)
文摘Through discussing the transformation of the invariant ideals, we firstly prove that the T-functor can only decrease the embedding dimension in the category of unstable algebras over the Steenrod algebra. As a corollary we obtain that the T-functor preserves the hypersurfaces in the category of unstable algebras. Then with the applications of these results to invariant theory, we provide an alternative proof that if the invariant of a finite group is a hypersurface, then so are its stabilizer subgroups. Moreover, by several counter-examples we demonstrate that if the invariants of the stabilizer subgroups or Sylow p-subgroups are hypersurfaces, the invariant of the group itself is not necessarily a hypersurface.
