Timeline for Specialization of PBW-algebras over rational function field
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 4, 2013 at 17:24 | vote | accept | MTS | ||
| Jul 4, 2013 at 17:24 | comment | added | MTS | I see, thanks very much for the explanation. That makes total sense. | |
| Jul 4, 2013 at 16:54 | comment | added | Vladimir Dotsenko | Matt, I am even more puzzled. The coefficients that arise are explicitly extracted from the reduction procedure I described (iteratively replacing $cm_1W_\lambda m_2$ by $cm_1f_\lambda m_2$). If $c$ has no pole at zero (which is true in the beginning before we started reducing), then, since coefficients of $f_\lambda$ do not have poles at zero, arising coefficients won't have poles at zero either. Really, part of the beauty here that besides being a theoretical result, Diamond lemma is most practical: it amounts to the fact that one can do long division. | |
| Jul 4, 2013 at 14:36 | comment | added | MTS | (The elements $d,e$ in my previous comment should be monomials, of course.) | |
| Jul 4, 2013 at 12:47 | comment | added | MTS | Vladimir, thanks for your answer. The potential problem I saw was in your "clearly". Saying that $a f_\sigma - f_\tau b$ can be reduced to zero means it is in the span of terms of the form $d(W_\mu - f_\mu)e$, where $d W_\mu e \leq a W_\sigma$. I had thought that perhaps coefficients could arise in that sum that had poles at $0$. It feels like this shouldn't be possible but I don't have a rigorous argument why not. | |
| Jul 4, 2013 at 11:36 | history | answered | Vladimir Dotsenko | CC BY-SA 3.0 |