Is there a standard notation for conjugation

1.3k Views Asked by At

I am using conjugation frequently in a paper, and I don't know the standard notation. Here http://mathworld.wolfram.com/Conjugation.html they use the notation $\phi_x(g)=xgx^{-1}$, but here https://en.wikipedia.org/wiki/Adjoint_representation they use the notation $\psi_g(h)=ghg^{-1}$. Here https://groupprops.subwiki.org/wiki/Group_acts_as_automorphisms_by_conjugation they use the notation $c_g$. I know this is related to the adjoint representation of a Lie group, but I'm not sure that the adjoint representation is appropriate here. Any help would be appreciated.

1

There are 1 best solutions below

12
On BEST ANSWER

Group theorists often use $g^x$ as shorthand for $x^{-1}gx$. Then $$g^{xy}=y^{-1}x^{-1}gxy=y^{-1}g^xy=(g^x)^y$$ etc.