Why Is the Notation for 2E6 Not Standardized?

💡 The Answer

• Some authors write it as 2E6(K), viewing it as an algebraic group over K.
• Others write it as 2E6(L), viewing it as a subgroup of E6(L).
• The subgroup is fixed by an outer involution.
• This ambiguity stems from the quadratic extension K⊂L.