Timeline for Cohomology algebra of the maximal nilpotent subalgebra of a semisimple Lie algebra
Current License: CC BY-SA 4.0
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| Apr 22, 2021 at 6:08 | comment | added | Vladimir Dotsenko | @YCor : for the right hand side, the most classical description of that algebra is, of course, as coinvariants of the Weyl group action on the Cartan subalgebra, that is $\mathbb{C}[\mathfrak{h}]/(\mathbb{C}[\mathfrak{h}]^W_+)$, and the grading by the integer lattice in the Cartan subalgebra seems to disappear in the quotient. That said, it is indeed a completely separate question, I think, since the algebra structures on the right and on the left are quite drastically different from the very beginning. | |
| Apr 21, 2021 at 15:16 | comment | added | YCor | I don't know if it's of interest here, but such a nilpotent Lie algebra admits a natural grading in a free abelian group of rank $\mathrm{rank}(\mathfrak{g})$, coming from the action of the maximal torus normalizing $\mathfrak{n}$. So the whole cohomology algebra inherits this grading, and one can wonder whether it makes sense at the level of the right hand de Rham cohomology space. | |
| Apr 21, 2021 at 15:06 | history | edited | Vladimir Dotsenko | CC BY-SA 4.0 |
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| Apr 18, 2021 at 20:49 | comment | added | user108998 | Thanks, don't know why I didn't see that! | |
| Apr 18, 2021 at 16:19 | comment | added | Vladimir Dotsenko | @EBz because elements of cohomological degree one anticommute and elements of cohomological degree two commute? | |
| Apr 18, 2021 at 12:05 | comment | added | user108998 | Why does the fact that the grading scales by 2 imply that the multiplicative structure cannot be preserved? | |
| Apr 18, 2021 at 7:01 | history | edited | Vladimir Dotsenko | CC BY-SA 4.0 |
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| Apr 18, 2021 at 6:52 | history | edited | YCor | CC BY-SA 4.0 |
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| Apr 18, 2021 at 6:51 | history | edited | Vladimir Dotsenko | CC BY-SA 4.0 |
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| Apr 18, 2021 at 6:44 | history | asked | Vladimir Dotsenko | CC BY-SA 4.0 |