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Graded Morita equivalences for generic Artin-Schelter regular algebras. (English) Zbl 1228.16024

In the main result of this paper, Theorem 3.1, the author proves that the conditions
(A)
Two generic 3-dimensional Noetherian Artin-Schelter algebras \(A=\mathcal A(E,\sigma)\) and \(A'=\mathcal A(E',\sigma')\) are Morita equivalent, and
(B)
The corresponding graded algebras \(\mathcal A(E,\nu^*\sigma^n)\) and \(\mathcal A(E',(\nu')^*(\sigma')^n)\) are isomorphic,
are equivalent.
Moreover, if \(A\) and \(A'\) are \(n\)-dimensional skew polynomial algebras then (A) implies (B) (Theorem 4.1). The converse of Theorem 4.1 is not true, as it is proved in Example 4.2.

MSC:

16S38 Rings arising from noncommutative algebraic geometry
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
16W50 Graded rings and modules (associative rings and algebras)
16D90 Module categories in associative algebras
16S36 Ordinary and skew polynomial rings and semigroup rings
16S37 Quadratic and Koszul algebras
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References:

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