Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graded twisted Calabi-Yau algebras are generalized Artin-Schelter
  regular   This is a general study of twisted Calabi-Yau algebras that are
$\mathbb{N}$-graded and locally finite-dimensional, with the following major
results. We prove that a locally finite graded algebra is twisted Calabi-Yau if
and only if it is separable modulo its graded radical and satisfies one of
several suitable generalizations of the Artin-Schelter regularity property,
adapted from the work of Martinez-Villa as well as Minamoto and Mori. We
characterize twisted Calabi-Yau algebras of dimension 0 as separable
$k$-algebras, and we similarly characterize graded twisted Calabi-Yau algebras
of dimension 1 as tensor algebras of certain invertible bimodules over
separable algebras. Finally, we prove that a graded twisted Calabi-Yau algebra
of dimension 2 is noetherian if and only if it has finite GK dimension.

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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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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
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The categories of this paper are: nucl-ex