Please.. can you give me a soft explaination?
\( f \) is meant to be a fractional (half) iterate of exp?
How do you arrive at \( f ( f^{\circ -1}(a) + f^{\circ -1}(b) ) = a + b \)? is the starting Hypotesis?
After that i can't follow the differentiation argument (my fault)...seems me that you are proving that whenerever f is an addition automorphism it is linear but is obvious that if \( f(x) \) is \( Cx \) for some \( C \) it is an automorphism of the addition...
in other words I don't get why we need such automorphism \( f \)...and how it helps us.
\( f \) is meant to be a fractional (half) iterate of exp?
How do you arrive at \( f ( f^{\circ -1}(a) + f^{\circ -1}(b) ) = a + b \)? is the starting Hypotesis?
After that i can't follow the differentiation argument (my fault)...seems me that you are proving that whenerever f is an addition automorphism it is linear but is obvious that if \( f(x) \) is \( Cx \) for some \( C \) it is an automorphism of the addition...
in other words I don't get why we need such automorphism \( f \)...and how it helps us.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)