Drinfeld orbifold algebras
Drinfeld orbifold algebras
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德林费尔德环折代数
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
S. Witherspoon
中科院分区：
文献类型：
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作者：
A. V. Shepler;S. Witherspoon
我们将Drinfeld-orbiold代数定义为滤子代数，它使有限群在多项式环上的作用产生的斜群代数(半直积)变形。它们同时推广了Weyl代数、分次(或Drinfeld)Hecke代数、有理Cherednik代数、辛反射代数和具有群作用的李代数的泛包络代数。我们给出了定义参数的充要条件，从而得到了两种一般形式的Drinfeld-orbiold代数，包括代数形式和同调形式。我们的代数条件适用于除两个以外的任何特征域，包括特征划分作用群的顺序的域。我们显式地解释了Hochschild上同调和Poincare-Birkhoff-Witt性质之间的联系(使用Gertenhaber括号)。我们还将产生的斜群代数的变形归类为Drinfeld-orbinold代数，并给出了它在交换群上的应用。
We define Drinfeld orbifold algebras as filtered algebras deforming the skew group algebra (semi-direct product) arising from the action of a finite group on a polynomial ring. They simultaneously generalize Weyl algebras, graded (or Drinfeld) Hecke algebras, rational Cherednik algebras, symplectic reflection algebras, and universal enveloping algebras of Lie algebras with group actions. We give necessary and sufficient conditions on defining parameters to obtain Drinfeld orbifold algebras in two general formats, both algebraic and homological. Our algebraic conditions hold over any field of characteristic other than two, including fields whose characteristic divides the order of the acting group. We explain the connection between Hochschild cohomology and a Poincare-Birkhoff-Witt property explicitly (using Gerstenhaber brackets). We also classify those deformations of skew group algebras which arise as Drinfeld orbifold algebras and give applications for abelian groups.