On the Cartan map for crossed products and Hopf-Galois extensions

群在交叉模系数下的非阿贝尔上同调与伽罗瓦上同调

Non-abelian hypercohomology of a group with coefficients in a crossed module, and Galois cohomology

发展了群在交叉模系数下的上同调理论，并应用于定义约化代数群伽罗瓦上同调的阿贝尔化映射。

幺半范畴的作用与Cartan型李代数的表示

Actions of monoidal categories and representations of Cartan type Lie algebras

本文通过交叉同态建立幺半范畴作用，统一构造Lie-Rinehart代数及Leibniz对的弱表示与容许表示，并引入交叉同态上同调理论以研究其形变，同时为广义Witt代数等提供新表示。

Galois groups and group actions on Lie algebras

If $\mathfrak{g} \subseteq \mathfrak{h}$ is an extension of Lie algebras over a field $k$ such that ${\rm dim}_k (\mathfrak{g}) = n$ and ${\rm dim}_k (\mathfrak{h}) = n + m$, then the Galois group ${\rm Gal} \, (\mathfrak{h}/\mathfrak{g})$ is explicitly described as a subgroup of the canonical semidirect product of groups ${\rm GL} (m, \, k) \rtimes {\rm M}_{n\times m} (k)$. An Artin type theorem for Lie algebras is proved: if a group $G$ whose order isinvertible in $k$ acts as automorphisms on a Lie algebra $\mathfrak{h}$, then $\mathfrak{h}$ is isomorphic to a skew crossed product $\mathfrak…

Subgroup depth and twisted coefficients

Danz computes the depth of certain twisted group algebra extensions in Comm. Alg. (2011), which are less than the values of the depths of the corresponding untwisted group algebra extensions in Burciu et al, I.E.J.A. (2011). In this paper, we show that the closely related h-depth of any group crossed product algebra extension is less than or equal to the h-depth of the corresponding (finite rank) group algebra extension. A convenient theoretical underpinning to do so is provided by the entwining structure of a right $H$-comodule algebra A and a right H-module coalgebra C for a Hopf algebra H. …

无对径的Hopf代数胚的裂扩张

Cleft Extensions for Hopf Algebroids without Antipodes

本文引入无对径Hopf代数胚的裂扩张，证明其与σ-扭曲交叉积、带正规基的Hopf-Galois扩张等价，研究相关Ehresmann Hopf代数胚的同构性，推广了相关理论。

Primitive ideals in Hopf algebra extensions

Let $H$ be a finite-dimensional Hopf algebra. We study the behaviou r of primitive and maximal ideals in certain types of ring extensions determined by $H$. The main focus is on the class of faithfully flat Galois extensions, which includes includes smash and crossed products. It is shown how analogous results can be obtained for the larger class of extensions possessing a total integral, which includes extensions $A^H\subseteq A $ when $H$ is semisimple. We use Passman's "primitivity machine" to reduce the whole theory of Kr ull relations for prime ideals to the case of primitive ideals. The …