Let A be a subalgebra of uq（sl（2）） generated by K, K-1 and F and A^δ be a subalgebra of b/q（sl（2）） generated by K, K-1 （and also Fd if q is a primitive d-th root of unity with d an odd number）. Given an Aδ...Let A be a subalgebra of uq（sl（2）） generated by K, K-1 and F and A^δ be a subalgebra of b/q（sl（2）） generated by K, K-1 （and also Fd if q is a primitive d-th root of unity with d an odd number）. Given an Aδ-module M, a/gq（s/（2））-module A A M is constructed via the iterated Ore extension of Uq（S/（2）） in a unified framework for any q. Then all the submodules of A δA5 M are determined for a fixed finite-dimensional indecomposable Aδ-module .M. It turns out that for some indecomposable A^-module M, the 5/q（sl（2））-module A @A M is indecomposable, which is not in the BGG-categories associated with quantum groups in general.展开更多
The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra from a Clifford monoid S =[Y; Gα. φα,β]by Ore-extensions, and to obtain a co-Frobenius semilat...The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra from a Clifford monoid S =[Y; Gα. φα,β]by Ore-extensions, and to obtain a co-Frobenius semilattice graded weak Hopf algebra H（S, n, c, x, a, b） through factoring At by a semilattice graded weak Hopf ideal.展开更多
A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorph...A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorphism and δ an α- derivation of a ring R. We prove that （1） If R is an （α, δ）-compatible and weakly 2-primal ring, then R[x; α, δ] is weakly semicommutative; （2） If R is （α, δ）-compatible, then R is weakly 2-primal if and only if R[x; α, δ] is weakly 2-primal.展开更多
A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper ...A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.展开更多
We compute the derivations of the positive part of the two-parameter quantum group Ur,s（B3） and show that the Hochschild cohomology group of degree 1 of this algebra is a three- dimensional vector space over the bas...We compute the derivations of the positive part of the two-parameter quantum group Ur,s（B3） and show that the Hochschild cohomology group of degree 1 of this algebra is a three- dimensional vector space over the base field C. We also compute the groups of （Hopf） algebra automorphisms of the augmented two-parameter quantized enveloping algebra Ur,s（B3）.展开更多
In this paper we prove that under some natural conditions, the Ore extensions and skew Laurent polynomial rings are injectively homogeneous or homologically homogeneous if so are their coefficient rings. Specifically,...In this paper we prove that under some natural conditions, the Ore extensions and skew Laurent polynomial rings are injectively homogeneous or homologically homogeneous if so are their coefficient rings. Specifically, we prove that if R is a commutative Noetherian ring of positive characteristic, then A<sub>n</sub>（R）, the n<sup>th</sup> Weyl algebra over R, is injectively homogeneous （resp. homologically homogeneous） if R has finite injective dimension （resp. global dimension）.展开更多
基金Supported by National Natural Foundation of China (Grant No. 11171291)Doctorate Foundation (Grant No. 200811170001) Ministry of Education of China
文摘Let A be a subalgebra of uq（sl（2）） generated by K, K-1 and F and A^δ be a subalgebra of b/q（sl（2）） generated by K, K-1 （and also Fd if q is a primitive d-th root of unity with d an odd number）. Given an Aδ-module M, a/gq（s/（2））-module A A M is constructed via the iterated Ore extension of Uq（S/（2）） in a unified framework for any q. Then all the submodules of A δA5 M are determined for a fixed finite-dimensional indecomposable Aδ-module .M. It turns out that for some indecomposable A^-module M, the 5/q（sl（2））-module A @A M is indecomposable, which is not in the BGG-categories associated with quantum groups in general.
基金supported by the National Natural Science Foundation of China(11271318,11171296,and J1210038)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20110101110010)the Zhejiang Provincial Natural Science Foundation of China(LZ13A010001)
文摘The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra from a Clifford monoid S =[Y; Gα. φα,β]by Ore-extensions, and to obtain a co-Frobenius semilattice graded weak Hopf algebra H（S, n, c, x, a, b） through factoring At by a semilattice graded weak Hopf ideal.
基金The NSF(11071097,11101217)of Chinathe NSF(BK20141476)of Jiangsu Province
文摘A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorphism and δ an α- derivation of a ring R. We prove that （1） If R is an （α, δ）-compatible and weakly 2-primal ring, then R[x; α, δ] is weakly semicommutative; （2） If R is （α, δ）-compatible, then R is weakly 2-primal if and only if R[x; α, δ] is weakly 2-primal.
基金The NSF(11471108) of Chinathe NSF(2015JJ2051,2016JJ2050) of Hunan Provincethe Teaching Reform Foundation(G21316) of Hunan Province
文摘A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.
基金supported by Specialized Research Fund for the Doctoral Program of Highter Education(Grant No.20130031110005)supported by NSFC(Grant No.11271131)
文摘We compute the derivations of the positive part of the two-parameter quantum group Ur,s（B3） and show that the Hochschild cohomology group of degree 1 of this algebra is a three- dimensional vector space over the base field C. We also compute the groups of （Hopf） algebra automorphisms of the augmented two-parameter quantized enveloping algebra Ur,s（B3）.
文摘In this paper we prove that under some natural conditions, the Ore extensions and skew Laurent polynomial rings are injectively homogeneous or homologically homogeneous if so are their coefficient rings. Specifically, we prove that if R is a commutative Noetherian ring of positive characteristic, then A<sub>n</sub>（R）, the n<sup>th</sup> Weyl algebra over R, is injectively homogeneous （resp. homologically homogeneous） if R has finite injective dimension （resp. global dimension）.
