Cocommutative Calabi–Yau Hopf algebras and deformations
Cocommutative Calabi–Yau Hopf algebras and deformations
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DOI：
10.1016/j.jalgebra.2010.06.010
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发表时间：
2009-06
影响因子：
0.9
通讯作者：
Ji-wei He;F. Oystaeyen;Yinhuo Zhang
中科院分区：
文献类型：
--
作者：
Ji-wei He;F. Oystaeyen;Yinhuo Zhang
利用最近引入的研究无穷维AS-Gorenstein Hopf代数的工具--同调积分，讨论了余交换Hopf代数的Calabi-Yau性质.证明了有限维李代数g的泛包络代数的斜群代数是Calabi-Yau当且仅当泛包络代数本身是Calabi-Yau且G是特殊线性群SL（g）的子群.描述了维数不大于3的Noether余交换Calabi-Yau Hopf代数.讨论了有限维李代数的Sridharan包络代数的Calabi-Yau性质。得到了Sridharan包络代数是Calabi-Yau的几个等价条件，从而部分回答了Berger提出的一个问题.我们列出了所有非同构的三维Calabi-Yau Sridharan包络代数。
The Calabi–Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group algebra of a universal enveloping algebra of a finite dimensional Lie algebra g with a finite subgroup G of automorphisms of g is Calabi–Yau if and only if the universal enveloping algebra itself is Calabi–Yau and G is a subgroup of the special linear group SL(g). The Noetherian cocommutative Calabi–Yau Hopf algebras of dimension not larger than 3 are described. The Calabi–Yau property of Sridharan enveloping algebras of finite dimensional Lie algebras is also discussed. We obtain some equivalent conditions for a Sridharan enveloping algebra to be Calabi–Yau, and then partly answer a question proposed by Berger. We list all the nonisomorphic 3-dimensional Calabi–Yau Sridharan enveloping algebras.