a expression in Group Theory

[princeton118]

What does this expression, SU(2,4), mean?

[CompuChip]

It's the notation for a specific group. Also see this Wikipedia page (http://en.wikipedia.org/wiki/Special_unitary_group), specifically under the "Generalized ... group" section.

[princeton118]

But in the Generalized Linear Group the second term in the parentheses is the Field. But here what does the "4" mean?

[morphism]

Probably the finite field with 4 elements.

[princeton118]

I see thanks!

[Chris Hillman]

Uh oh, hope the OP sees this! The special unitary group SU(p,q) is the unitary analog of the special orthogonal group SO(p,q). For example, SO(2,4) comes from the pseudo-euclidean inner product

\left(\vec{u}, \, \vec{v} \right) =
-u_1 \, v_1 - u_2 \, v_2 + u_3 \, v_3 + u_4 \, v_4 + u_5 \, v_5 + u_6 \, v_6

and SU(2,4) comes from the hermitian analog. The field is generally the complex numbers for unitary groups or real numbers for orthogonal groups, but other fields can be considered and then an extra letter is added to indicate this.

How annoying! The only hit Google gives me is " Generalized special unitary group" in this version of this WP article (http://en.wikipedia.org/w/index.php?title=Special_unitary_group&oldid=174713080) which I happen to know is basically correct, but do as I say not as I do: never cite Wikipedia articles because Wikipedia is unstable and unreliable! :grumpy: