Projectivity and freeness over comodule algebras

有限生成$(H, {\rm C})$-余模的自同态环上的投射性与平坦性

Projectivity and flatness over the endomorphism ring of a finitely generated $(H, {\mathcal C})$-comodule

设k为交换环，H为k上双代数，C为(H,A)-余环，若C作为左A-模平坦，有限生成的右(H,C)-余模Λ对应的自同态环上的模具有投射性与平坦性的充要条件被给出；当C含固定H-群样元时，可将Λ替换为A。

Projectivity of a relative Hopf module over the subring of coinvariants

Let $k$ be a commutative ring, $H$ a faithfully flat Hopf algebra with bijective antipode, $A$ a $k$-flat right $H$-comodule algebra. We investigate when a relative Hopf module is projective over the subring of coinvariants $B=A^{{\rm co}H}$, and we study the semisimplicity of the category of relative Hopf modules.

Flatness and freeness properties of the generic Hopf Galois extensions

In previous work, to each Hopf algebra H and each invertible right two-cocycle on H, Eli Aljadeff and the first-named author attached a subalgebra B of the free commutative Hopf algebra S generated by the coalgebra underlying H; the algebra B is the subalgebra of coinvariants of a generic Hopf Galois extension. In this paper we give conditions under which S is faithfully flat, or even free, as a B-module. We also show that B is generated as an algebra by certain elements arising from the theory of polynomial identities for comodule algebras developped jointly with Aljadeff.

弱Hopf代数的Poisson $(A,H)$-Hopf模基本定理

Fundamental theorem of Poisson $(A,H)$-Hopf module for weak Hopf algebras

该研究将Poisson Hopf模基本定理推广至弱Hopf代数情形，同时推导了Poisson Hopf模范畴的相对投射性，拓展了相关代数结构理论的适用范围。

有限非结合代数的局部有限变种

Locally finite varieties of nonassociative algebras

本文研究有限域上非结合代数的局部有限变种，探讨其基本代数性质及数量比估计。

The Generating Condition for Coalgebras

For a ring $R$, the properties of being (left) selfinjective or being cogenerator for the left $R$-modules do not imply one another, and the two combined give rise to the important notion of PF-rings. For a coalgebra $C$, (left) self-projectivity implies that $C$ is generator for right comodules and the coalgebras with this property were called right quasi-co-Frobenius; however, whether the converse implication is true is an open question. We provide an extensive study of this problem. We show that this implication does not hold, by giving a large class of examples of coalgebras having the "ge…