Let W be an associative PI -affine algebra over a field F of characteristic zero. Suppose W is G-graded where G is a finite group. Let exp(W) and exp(We) denote the codimension growth of W and of the identity component We, respectively. We prove exp(W) ≤ |G|2 exp(W e). This inequality had been conjectured by Bahturin and Zaicev.
|Number of pages||10|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - Jul 2010|
- Graded algebra
- Polynomial identity