Tsukuba Journal of Mathematics

Geometric classification of quadratic algebras in two variables

Kenta Ueyama

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Abstract

In this paper, we classify quadratic algebras in two variables at two levels: (1) up to isomorphism of graded algebras, (2) up to graded Morita equivalence. In general, it is difficult to classify algebras by looking at generators and relations, so we take a geometric approach, namely, using point schemes defined by Artin, Tate and Van den Bergh, to complete the classification.

Article information

Source
Tsukuba J. Math., Volume 34, Number 1 (2010), 79-96.

Dates
First available in Project Euclid: 8 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1283967409

Digital Object Identifier
doi:10.21099/tkbjm/1283967409

Mathematical Reviews number (MathSciNet)
MR2723725

Zentralblatt MATH identifier
1204.16020

Subjects
Primary: 16S37: Quadratic and Koszul algebras
Secondary: 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]

Keywords
quadratic algebra graded Morita equivalence point scheme

Citation

Ueyama, Kenta. Geometric classification of quadratic algebras in two variables. Tsukuba J. Math. 34 (2010), no. 1, 79--96. doi:10.21099/tkbjm/1283967409. https://projecteuclid.org/euclid.tkbjm/1283967409


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