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AS-regularity of Geometric Algebras of Plane Cubic Curves

Let k be an algebraically closed field of characteristic 0 and A a graded k-algebra finitely generated in degree 1. In this paper, for 3-dimensional quadratic AS-regular algebras except for Type EC, we give a complete list of twisted superpotentials and a complete list of superpotentials such that derivation-quotient algebras are 3-dimensional quadratic Calabi-Yau AS-regular algebras. For an algebra A of Type EC, we give a criterion when A is AS-regular. As an application, for an algebra A of any type, we show that there exists a Calabi-Yau AS-regular algebra S such that A and S are graded Morita equivalent. This result tells us that, for a 3-dimensional quadratic AS-regular algebra A, to study the noncommutative projective scheme for A defined by Artin-Zhang is reduced to study the noncommutative projective scheme for S for the Calabi-Yau AS-regular algebra S.

Ketersediaan

Informasi Detail

Judul Seri

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY; Vol.112 Issue 2 April 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 193-217

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

ELLIPTIC CURVES
AS-REGULAR ALGEBRAS
CALABI–YAU ALGEBRAS
GEOMETRIC ALGEBRAS
KOSZUL ALGEBRAS
SUPERPOTENTIALS

Info Detail Spesifik

DOI: https://doi.org/10.1017/S1446788721000070

Pernyataan Tanggungjawab

Ayako Itaba, Masaki Matsuno

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