论文标题
$ A_1 $的理性Cherednik代数和分裂的权力
The Rational Cherednik Algebra of Type $A_1$ with Divided Powers
论文作者
论文摘要
由Cherednik代数理论的最新发展，我们以积极特征为基础，研究了具有分裂力量的理性Cherednik代数。在我们的研究中，我们从最简单的情况开始，即$ A_1 $的理性Cherednik代数。我们调查了其最大的分界功率扩展，超过$ r [c] $和$ r $，用于特征零的特征零$ r $。在这些情况下，我们证明，最大分配功率扩展是基本环上的免费模块，并在$ r [c] $的情况下构建明确的基础。此外，我们还为任意环上的$ a_1 $ type $ a_1 $的理性Cherednik代数提供了抽象的构造，并证明这种概括扩展了理性的Cherednik代数以包括所有分隔的权力。
Motivated by the recent developments of the theory of Cherednik algebras in positive characteristic, we study rational Cherednik algebras with divided powers. In our research we have started with the simplest case, the rational Cherednik algebra of type $A_1$. We investigate its maximal divided power extensions over $R[c]$ and $R$ for arbitrary principal ideal domains $R$ of characteristic zero. In these cases, we prove that the maximal divided power extensions are free modules over the base rings, and construct an explicit basis in the case of $R[c]$. In addition, we provide an abstract construction of the rational Cherednik algebra of type $A_1$ over an arbitrary ring, and prove that this generalization expands the rational Cherednik algebra to include all of the divided powers.
