Abstract
In this paper the Gel'fand-Kirillov dimension GKdim(A) is calculated for a relatively free associative algebra A over an arbitrary ground field. This dimension is determined by the complexity type of the algebra A or by the set of semidirect products of matrix algebras over a polynomial ring contained in the variety Var(A). The proof is comparatively elementary and does not use the local representability of relatively free algebras.
| Original language | English |
|---|---|
| Pages (from-to) | 1703-1726 |
| Number of pages | 24 |
| Journal | Sbornik Mathematics |
| Volume | 195 |
| Issue number | 11 |
| DOIs | |
| State | Published - 2004 |
| Externally published | Yes |