Truncated Quantum Drinfeld Hecke Algebras and Hochschild Cohomology
Truncated Quantum Drinfeld Hecke Algebras and Hochschild Cohomology
复制标题
截断量子 Drinfeld Hecke 代数和 Hochschild 上同调
DOI：
--
复制
发表时间：
2017
影响因子：
0.6
通讯作者：
Christine Uhl
中科院分区：
文献类型：
--
作者：
Lauren E. Grimley;Christine Uhl
我们考虑有限群扩张的量子外代数的形变。在这些变形中有一类代数，由于它们与经典Drinfeld Hecke代数的关系，我们称之为截断量子Drinfeld Hecke代数。利用Bergman的钻石引理，给出了这类代数存在的充要条件。通过计算相关的Hochschild上同调，明确了Hochschild上同调与截断量子Drinfeld-Hecke代数之间的联系。为了证明允许代数的方差，我们计算了两个经典类型的例子，并演示了一个不是作为量子Drinfeld Hecke代数的因子代数出现的例子。
We consider deformations of quantum exterior algebras extended by finite groups. Among these deformations are a class of algebras which we call truncated quantum Drinfeld Hecke algebras in view of their relation to classical Drinfeld Hecke algebras. We give the necessary and sufficient conditions for which these algebras occur, using Bergman’s Diamond Lemma. We compute the relevant Hochschild cohomology to make explicit the connection between Hochschild cohomology and truncated quantum Drinfeld Hecke algebras. To demonstrate the variance of the allowed algebras, we compute both classical type examples and demonstrate an example that does not arise as a factor algebra of a quantum Drinfeld Hecke algebra.