Timeline for Universal enveloping ring–symmetric algebra isomorphism for Lie rings
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 8, 2012 at 11:29 | comment | added | grok | Clarification: I consider algebras over $\mathbb Z$, in which case Lazard shows that there is a ring isomorphism between $gr(U(g))$ and $S(g)$. Indeed $\mathbb Z$ is a PID. The typical "counterexamples" to PBW involve algebras over non-domains such as $\mathbb F_p[a,b,c]/(a^p,b^p,c^p)$. My question is about isomorphism of $S(g)$ and $U(g)$ as abelian groups, not as rings. | |
| Aug 7, 2012 at 12:57 | answer | added | Bugs Bunny | timeline score: 4 | |
| Aug 7, 2012 at 12:53 | comment | added | Bugs Bunny | Doc, you make my head spin. Surely, PBW holds over any field. | |
| Aug 6, 2012 at 14:18 | answer | added | Vladimir Dotsenko | timeline score: 0 | |
| Aug 6, 2012 at 10:43 | comment | added | Alexander Chervov | Just remark isomorphism fails for char = p mathoverflow.net/questions/99018/… | |
| Aug 6, 2012 at 9:32 | history | asked | grok | CC BY-SA 3.0 |