Timeline for A potential resolution of $R/r$
Current License: CC BY-SA 3.0
5 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Jun 14, 2011 at 16:33 | vote | accept | Greg Muller | ||
| Jun 14, 2011 at 7:09 | answer | added | Vladimir Dotsenko | timeline score: 6 | |
| Jun 14, 2011 at 1:55 | comment | added | Tyler Lawson |
I don't have an answer for your question. If R is a free algebra with r mapping to one of the generators, then the higher homology groups all vanish (this is because R is the free DGA on a chain complex weakly equivalent to a complex in degree zero obtained by forgetting the generators). I'm pretty sure that this means you're computing the derived pushout of $k\leftarrow k[x]\to R$ in associative DGAs, where $x\mapsto r$. This, to me, suggests that the higher homology groups may be simply "what they are". (Also, if r is any unit, $H_n$ is an $H_0=0$-module and so is zero.)
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| Jun 13, 2011 at 21:44 | history | asked | Greg Muller | CC BY-SA 3.0 |