Gelfand-Kirillov dimensions of a tensor product (Q1077509)

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.