Is it possible ?


Rather obviously yes.

Let $A$ be the algebra over the field $K$ generated by elements $a_1,a_2,\ldots,$ with $a_i$ in dimension $i$ and with $a_ia_j=0$ for all $i$ and $j$. This is an incredibly uninteresting example, but since each graded piece is one-dimensional, its Poincare series is $\sum_{n=0}^\infty t^n=1/(1-t)$.

  • $\begingroup$ I agree but I am interested with an algebra with non-trivial multiplication. $\endgroup$ – Melania Sep 29 '10 at 20:47
  • 3
    $\begingroup$ @Melania: how about start as Robin did, and then kill all $a_ia_ja_k$? $\endgroup$ – Hailong Dao Sep 29 '10 at 21:23
  • $\begingroup$ Yes..The Poincare series will be $\dfrac{1}{(1-t)(1-t^2)}.$ Thanks! $\endgroup$ – Melania Sep 29 '10 at 21:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.