Kyoto Journal of Mathematics

Graded Morita equivalences for generic Artin-Schelter regular algebras

Kenta Ueyama

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Abstract

Let A=A(E,σ),A'=A(E',σ') be Noetherian Artin-Schelter regular geometric algebras with dimkA1=dimkA1'=n, and let ν,ν' 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) A(E,νσn) is isomorphic to A(E',(ν')(σ')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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1303494511

Digital Object Identifier
doi:10.1215/21562261-1214420

Mathematical Reviews number (MathSciNet)
MR2793276

Zentralblatt MATH identifier
1228.16024

Subjects
Primary: 16W50: Graded rings and modules 16D90: Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality 16S38: Rings arising from non-commutative algebraic geometry [See also 14A22] 16S37: Quadratic and Koszul algebras

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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