For an algebraically closed field $F$, what is the dimension of $\operatorname{SL}(n,F)$ as an algebraic group? Can anyone refer me to a place in the literature where this is calculated?
2026-03-25 09:28:44.1774430924
The dimension of $\operatorname{SL}(n,F)$ as a linear algebraic group
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The dimension is $n^2-1$. It's a hypersurface in $F^{n^2}$ defined by the equation determinant${}=1$. Any text on linear algebraic groups, for instance that by Humphreys, will have this.