Timeline for Is the natural map from the free Lie algebra to the free associative algebra injective?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 2, 2021 at 18:33 | history | edited | LSpice | CC BY-SA 4.0 |
'by' didn't belong
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| Jul 2, 2021 at 18:17 | history | edited | Michael Hardy | CC BY-SA 4.0 |
\newcommand{\im}{\operatorname{im}}
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| Jul 2, 2021 at 18:10 | comment | added | Oliver Nash | @JoshuaMundinger thanks, looking at Bourbaki now, I think I see your point. $(A, \rho)$ is the universal enveloping algebra of $L$ and $L$ is projective (in fact free) as an $R$-module so by this beefed-up PBW $\rho$ is always injective! | |
| Jul 2, 2021 at 16:08 | comment | added | Joshua Mundinger | The PBW theorem holds for all coefficient rings for Lie algebras projective as $R$-modules. | |
| Jul 2, 2021 at 16:05 | history | asked | Oliver Nash | CC BY-SA 4.0 |