## Kyoto Journal of Mathematics

### Graded Morita equivalences for generic Artin-Schelter regular algebras

Kenta Ueyama

#### Abstract

Let $A=\mathcal{A}(E,\sigma),A'=\mathcal{A}(E',\sigma')$ be Noetherian Artin-Schelter regular geometric algebras with $\operatorname{dim}_{k}A_{1}=\operatorname{dim}_{k}A_{1}'=n$, and let $\nu,\nu'$ be generalized Nakayama automorphisms of $A,A'$. In this paper, we study relationships between the conditions

(A) $A$ is graded Morita equivalent to $A'$, and

(B) $\mathcal{A}(E,\nu^{*}\sigma^{n})$ is isomorphic to $\mathcal{A}(E',(\nu')^{*}(\sigma')^{n})$ as graded algebras.

It is proved that if $A,A'$ are “generic” 3-dimensional quadratic Artin-Schelter regular algebras, then (A) is equivalent to (B), and if $A,A'$ are $n$-dimensional skew polynomial algebras, then (A) implies (B).

#### Article information

Source
Kyoto J. Math., Volume 51, Number 2 (2011), 485-501.

Dates
First available in Project Euclid: 22 April 2011

https://projecteuclid.org/euclid.kjm/1303494511

Digital Object Identifier
doi:10.1215/21562261-1214420

Mathematical Reviews number (MathSciNet)
MR2793276

Zentralblatt MATH identifier
1228.16024

#### Citation

Ueyama, Kenta. Graded Morita equivalences for generic Artin-Schelter regular algebras. Kyoto J. Math. 51 (2011), no. 2, 485--501. doi:10.1215/21562261-1214420. https://projecteuclid.org/euclid.kjm/1303494511

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