On the restricted Jordan plane in odd characteristic

On the double of the (restricted) super Jordan plane

We consider the super Jordan plane, a braided Hopf algebra introduced--to the best of our knowledge--in works of N. Andruskiewitsch, I. Angiono, I. Heckenberger, and its restricted version in odd characteristic introduced by the same authors. We show that their Drinfeld doubles give rise naturally to Hopf superalgebras justifying a posteriori the adjective super given in their work. These Hopf superalgebras are extensions of super commutative ones by the enveloping, respectively restricted enveloping, algebra of $\mathfrak{osp}(1|2)$.

关于特征$2$下受限Jordan平面的Drinfeld double

On the Drinfeld double of the restricted Jordan plane in characteristic $2$

本文研究特征2下受限Jordan平面的Drinfeld double，证明其可纳入一个Hopf代数正合序列，并显式计算了相关5维受限Lie代数的不可分解模。

Modular Quantizations of Lie Algebras of Cartan Type K via Drinfeld Twists of Jordanian Type

We construct explicit Drinfel'd twists of Jordanian type for the generalized Cartan type K Lie algebras in characteristic 0 and obtain the corresponding quantizations, especially their integral forms. By making modular reductions including modulo p and modulo p-restrictedness reduction, and base changes, we derive certain modular quantizations of the restricted universal enveloping algebra $\mathbf u(\mathbf{K}(2n{+}1;\underline{1}))$ for the restricted simple Lie algebra of Cartan type K in characteristic p. They are new pointed Hopf algebras of noncommutative and noncocommutative and with di…

Modular quantizations of Lie algebras of Cartan type $H$ via Drinfeld Twists

We construct explicit Drinfel'd twists for the generalized Cartan type $H$ Lie algebras in characteristic $0$ and obtain the corresponding quantizations and their integral forms. Via making modular reductions including modulo $p$ reduction and modulo $p$-restrictedness reduction, and base changes, we derive certain modular quantizations of the restricted universal enveloping algebra $\mathbf u(\mathbf{H}(2n;\underline{1}))$ in characteristic $p$. They are new non-pointed Hopf algebras of truncated $p$-polynomial noncommutative and noncocommutative deformation of prime-power dimension $p^{p^{2n…

关于玻色化上同调的有限生成性

On the finite generation of the cohomology of bosonizations

该研究拓展已有结果，利用（霍普夫）代数的形变序列证明合适的辫子霍普夫代数经有限维霍普夫代数玻色化后上同调有限生成，结果可推广至smash积，还复现了已知结论并给出新的例子。

单位根处非展开限制量子群的权模范畴

Categories of Weight Modules for Unrolled Restricted Quantum Groups at Roots of Unity

本文研究任意单位根处非展开限制量子群的权模范畴，证明辫群作用自然延拓，范畴为具有平凡Müger中心的通常半单辫子范畴，且投射覆盖自对偶，并联系高秩单态顶点算子代数。