Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: m-Koszul Artin-Schelter regular algebras   This paper studies the homological determinants and Nakayama automorphisms of
not-necessarily-noetherian $m$-Koszul twisted Calabi-Yau or, equivalently,
$m$-Koszul Artin-Schelter regular, algebras. Dubois-Violette showed that such
an algebra is isomorphic to a derivation quotient algebra D(w,i) for a
unique-up-to-scalar-multiples twisted superpotential w in a tensor power of
some vector space V. By definition, D(w,i) is the quotient of the tensor
algebra TV by the ideal generated by all i-th order left partial derivatives of
w. We identify the group of graded algebra automorphisms of D(w,i) with a
subgroup of GL(V). We show that the homological determinant of a graded algebra
automorphism $\sigma$ of an $m$-Koszul Artin-Schelter regular algebra D(w,i) is
the scalar hdet($\sigma$) given by the formula hdet($\sigma$) w
=$\sigma^{\otimes m+i}$(w). It follows from this that the homological
determinant of the Nakayama automorphism of an $m$-Koszul Artin-Schelter
regular algebra is 1. As an application, we prove that the homological
determinant and the usual determinant coincide for most quadratic noetherian
Artin-Schelter regular algebras of dimension 3.

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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph