Gelfand-Kirillov dimensions of a tensor product
type: Item
instance of: scholarly article
title: Gelfand-Kirillov dimensions of a tensor product
zbMATH Open document ID: 0595.16019
DOI: 10.1007/BF01161917
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173850
review text: Let \(2\leq \alpha \leq \beta\) be real numbers. \textit{R. B. Warfield} [Math. Z. 185, 411-447 (1984; Zbl 0506.16017)] asked whether for any \(\gamma\), \(2+\beta \leq \gamma \leq \alpha +\beta\) there exist algebras A,B of Gelfand-Kirillov dimension \(\alpha\),\(\beta\) respectively, such that \(A\otimes B\) has dimension \(\gamma\). Considering the lower Gelfand- Kirillov dimension we answer this question affirmatively. Further we show that the two dimensions independently admit all values allowed in the class of tensor products.
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16W99
Mathematics Subject Classification ID: 16P60
zbMATH DE Number: 3957357
zbMATH Keywords: lower Gelfand-Kirillov dimension
zbMATH Keywords: tensor products
author: Jan Krempa
author: Jan Okniński
MaRDI profile type: Publication
cites work: Q3677877
description: scientific article; zbMATH DE number 3957357