Let H be a finite dimensional Hopf algebra over a field and A an H-module algebra. The H induces an action on the CA#H(A) by adjoint and CA#H(A)H= Z(A # H) = C,where CA#H(A) denotes the centralizer which algebra A in ...Let H be a finite dimensional Hopf algebra over a field and A an H-module algebra. The H induces an action on the CA#H(A) by adjoint and CA#H(A)H= Z(A # H) = C,where CA#H(A) denotes the centralizer which algebra A in A # H and Z(A # H) the center of A # H.The aim of this paper is to discuss ,the Galois conditions on the centralizer CA# H(A).We prove that CA# H(A)/ZA # H is H* -Galois if and only if CA# H(A)# H/CA# H(A) is H-separable). Furthermore , if H is a finite dimensional semisimple Hopf algebra and CA# H(A)# H is an Azumaya C-algebra or A # H/A is H-separable, CA# H(A) satisfies the double centralizer property in CA# H(A)# H, CA# H(A)/C is separable and there exists a cocommutative left integral t ∈∫1H,then CA# H(A)/C is H*-Galois.展开更多
Let B and H be finitely generated projective Hopf algebras over a commutative ring R, with B cocommutative and H commutative. In this paper we investigate cocleft extensions of Hopf algebras, and prove that the isomor...Let B and H be finitely generated projective Hopf algebras over a commutative ring R, with B cocommutative and H commutative. In this paper we investigate cocleft extensions of Hopf algebras, and prove that the isomorphism classes of cocleft Hopf algebras extensions of B by H are determined uniquely by the group C(B, H) = ZC(B, H)/d(B, H) .展开更多
A method of predicting design pressure and burn-through of in-service welding pipes was established.Temperature distributions of in-service welding under variable parameters were simulated by FEM.The effect of flowing...A method of predicting design pressure and burn-through of in-service welding pipes was established.Temperature distributions of in-service welding under variable parameters were simulated by FEM.The effect of flowing of internal media was regarded as forced convection.Based on the numerical results,design pressure of the pipe can be obtained and burn-through can be predicted.It can be concluded that the design pressure decreases with the increasing of heat input.RSF and design pressure of the pipe increase with the increasing of flow rate.There is a range in which the increase changes greatly.For in-service welding,the range should be considered adequately to determine operating condition optimally.RSF increases with the increasing of pipe wall thickness.While the thickness increases to an extent,RSF shows little increase.Accord-ing to the curves of design pressure versus different parameters,safe working pressure can be achieved.展开更多
文摘Let H be a finite dimensional Hopf algebra over a field and A an H-module algebra. The H induces an action on the CA#H(A) by adjoint and CA#H(A)H= Z(A # H) = C,where CA#H(A) denotes the centralizer which algebra A in A # H and Z(A # H) the center of A # H.The aim of this paper is to discuss ,the Galois conditions on the centralizer CA# H(A).We prove that CA# H(A)/ZA # H is H* -Galois if and only if CA# H(A)# H/CA# H(A) is H-separable). Furthermore , if H is a finite dimensional semisimple Hopf algebra and CA# H(A)# H is an Azumaya C-algebra or A # H/A is H-separable, CA# H(A) satisfies the double centralizer property in CA# H(A)# H, CA# H(A)/C is separable and there exists a cocommutative left integral t ∈∫1H,then CA# H(A)/C is H*-Galois.
基金the NSF of China(No.10571153)and the NSF(No.2004kj352) of Anhui ProvinceChina
文摘Let B and H be finitely generated projective Hopf algebras over a commutative ring R, with B cocommutative and H commutative. In this paper we investigate cocleft extensions of Hopf algebras, and prove that the isomorphism classes of cocleft Hopf algebras extensions of B by H are determined uniquely by the group C(B, H) = ZC(B, H)/d(B, H) .
基金This work was supported by SINOPEC(Grant No.304001)Doctorate Creation Foundation of Nanjing University of Technology(Grant No.BSCX200511).
文摘A method of predicting design pressure and burn-through of in-service welding pipes was established.Temperature distributions of in-service welding under variable parameters were simulated by FEM.The effect of flowing of internal media was regarded as forced convection.Based on the numerical results,design pressure of the pipe can be obtained and burn-through can be predicted.It can be concluded that the design pressure decreases with the increasing of heat input.RSF and design pressure of the pipe increase with the increasing of flow rate.There is a range in which the increase changes greatly.For in-service welding,the range should be considered adequately to determine operating condition optimally.RSF increases with the increasing of pipe wall thickness.While the thickness increases to an extent,RSF shows little increase.Accord-ing to the curves of design pressure versus different parameters,safe working pressure can be achieved.
