Derivations of the Positive Part of the Two-parameter Quantum Group of type $G_2$

量子幂零代数的导子与Hochschild上同调

Derivations and Hochschild cohomology of quantum nilpotent algebras

本文在中心满足技术性假设的条件下计算了量子幂零代数的导子，并由此显式描述了量子包络代数正部分的第一Hochschild上同调群，方法上利用了Goodearl和Yakimov构造的初始cluster。

Abelianizations of derivation Lie algebras of the free associative algebra and the free Lie algebra

We determine the abelianizations of the following three kinds of graded Lie algebras in certain stable ranges: derivations of the free associative algebra, derivations of the free Lie algebra and symplectic derivations of the free associative algebra. In each case, we consider both the whole derivation Lie algebra and its ideal consisting of derivations with positive degrees. As an application of the last case, and by making use of a theorem of Kontsevich, we obtain a new proof of the vanishing theorem of Harer concerning the top rational cohomology group of the mapping class group with respec…

Kontsevich辛导子李代数交换情形的第二同调群

The second homology group of the commutative case of Kontsevich's symplectic derivation Lie algebra

针对Kontsevich辛导子李代数交换情形的正权部分整体同调群研究不足的问题，利用辛群经典表示理论与权分次分解，确定了其第二同调群。