Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Skew derivations on generalized Weyl algebras   A wide class of skew derivations on degree-one generalized Weyl algebras
$R(a,\varphi)$ over a ring $R$ is constructed. All these derivations are
twisted by a degree-counting extensions of automorphisms of $R$. It is
determined which of the constructed derivations are $Q$-skew derivations. The
compatibility of these skew derivations with the natural ${\mathbb Z}$-grading
of $R(a,\varphi)$ is studied. Additional classes of skew derivations are
constructed for generalized Weyl algebras given by an automorphism $\varphi$ of
a finite order. Conditions that the central element $a$ that forms part of the
structure of $R(a,\varphi)$ need to satisfy for the orthogonality of pairs of
aforementioned skew derivations are derived. General constructions are
illustrated by classification of skew derivations of generalized Weyl algebras
over the polynomial ring in one variable and with a linear polynomial as the
central element.

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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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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: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio