Segre product of Artin-Schelter regular algebras of dimension 2 and embeddings in quantum \(\mathbb{P}^ 3\)'s
type: Item
instance of: scholarly article
title: Segre product of Artin-Schelter regular algebras of dimension 2 and embeddings in quantum \(\mathbb{P}^ 3\)'s
zbMATH Open document ID: 0853.17012
author: Kristel Van Rompay
published in: Journal of Algebra
publication date: 1996-06-05T00:00:00Z
review text: Let \(A,B\) be two quantum planes; they are quadratic AS-regular algebras of global dimension 2 [see \textit{M. Artin} and \textit{W. Schelter}, Adv. Math. 66, 171-216 (1987; Zbl 0633.16001)]. In this paper all the embeddings of the Segre product \(A \circ B = \oplus_{i \geq 0} A_i \otimes B_i\) on quantum \(\mathbb{P}^3\)'s are listed. Here ``quantum \(\mathbb{P}^3\)'' means a quadratic AS-regular algebra \(C\) of global dimension 4, and ``embedding'' means a graded, degree zero, surjective algebra map \(C \to A \circ B\) such that \(C_1 \simeq A_1 \otimes B_1\) [see \textit{M. Artin} and \textit{J. J. Zhang}, Adv. Math. 109, 228-287 (1994; Zbl 0833.14002)]. Schelter's computer program Affine was used to prove that the list contains all such embeddings. See also [\textit{M. Vancliff} and the author, Embedding a quantum non-singular quadric in a quantum \(\mathbb{P}^3\), Preprint (1995)].
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 14A22
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 869789
zbMATH Keywords: quadratic Artin-Schelter regular algebras
zbMATH Keywords: quantum projective spaces
zbMATH Keywords: Segre product
zbMATH Keywords: quantum planes
zbMATH Keywords: embeddings
reviewed by: Nicolás Andruskiewitsch
MaRDI profile type: Publication
full work available at URL: jabr.1996.0078
OpenAlex ID: W1990437823
DOI: 10.1006/JABR.1996.0078
description: scientific article; zbMATH DE number 869789