nLab projective special linear group

1. Definition

The projective general special linear group $PSL(n)$ (in some dimension $n$ and over some coefficients) is the quotient group of the special linear group $SL(n)$ by its center.

2. Examples

• there is an exceptional isomorphism between the rotational icosahedral group $I$ and the projectiver special linear group in dimension 2 with coefficients in a prime field: $I \simeq PSL_2(\mathbb{F}_5)$ (this Prop.)

• the automorphism group of the Fano plane is $\simeq PSL(2,\mathbb{F}_7)$ (…)

3. Related concepts

• projective general linear group

• projective space

4. References

• Wikipedia, Projective linear group