I'd like to solicit good notations for the abelianization of a Lie algebra $\mathfrak g$. One could write $\mathfrak g/[\mathfrak g,\mathfrak g]$, or even $H_1(\mathfrak g)$ but I'd like something that is relatively compact. I've been using $\mathfrak g_{ab}$, but that strikes me as a bit ugly.
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$\begingroup$ I write $G^{ab}$ in the case of groups; what is so ugly about it? $\endgroup$– Martin BrandenburgCommented Nov 3, 2010 at 13:42
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$\begingroup$ Possibly the mismatch of the font. $\endgroup$– Jim ConantCommented Nov 3, 2010 at 14:07
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1$\begingroup$ \mathfrak h, perhaps? $\endgroup$– Ben Webster ♦Commented Nov 3, 2010 at 14:08
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8$\begingroup$ Maximal semisimple quotient is $\mathfrak{g}^{\rm{ss}}$, so for maximal abelian quotient why not $\mathfrak{g}^{\rm{ab}}$? (Note: Roman font for superscript, not italics.) $\endgroup$– BCnrdCommented Nov 3, 2010 at 15:18
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$\begingroup$ Yeah, maybe changing the font is the simplest answer. $\endgroup$– Jim ConantCommented Nov 3, 2010 at 15:36
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