After reading [this][1] question I was wondering whether mathematicians tried to invent better names for exceptional simple Lie groups $F_4, E_6, E_7, E_8$ ? These names seems a bit obscure and does not show that we have a series here of four groups. This series is of course different than infinite series $SO_n,SU_n,Sp_n$ (pardon, it seems there is no plural form for "series" in English, in Polish there is). Letters $A,B,C,D,E,F,G$ are OK to use for Killing and Cartan who were classifying all simple compact Lie groups. Now we could have better names showing that these groups are groups of isometries of series of projective spaces over algebras being tensor product of octonions with real, complex, quaternion and octonion algebra. This is materialized in **Freudenthal magic square**. However letters used in magic square do not seem to represent the symmetry. For example first row is: $A_1,A_2,C_3,F_4$. In other words we can name it: $SO_3,SU_3,Sp_3,F_4$. It is not reflecting fact that position $k,n$ in magic square represent tensor product of division algebras $\mathcal A_k\otimes\mathcal A_n$ where $k,n=1,2,4,8$ where I denoted by $\mathcal A_k$ reals, complex numbers, quaternions or octonions.

The effort of better naming shouldn't be undervalued. By naming groups properly we also understand them better. Do you agree ?


  [1]: https://mathoverflow.net/questions/179141/who-originated-the-standard-symbols-for-lie-groups-gl-sl-su-etc