Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Rational Cherednik Algebra of Type $A_1$ with Divided Powers   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.

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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: stat