Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity criterion and classification for algebras of Jordan type   We show that Artin-Schelter regularity of a $\mathbb{Z}$-graded algebra can
be examined by its associated $\mathbb{Z}^r$-graded algebra. We prove that
there is exactly one class of four-dimensional Artin-Schelter regular algebras
with two generators of degree one in the Jordan case. This class is strongly
noetherian, Auslander regular, and Cohen-Macaulay. Their automorphisms and
point modules are described.

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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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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: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph