Cayley 1845 / Dickson 1919 doubling procedure: from a *-algebra A constructs a 2-dim *-algebra A x A; iterating from R produces C, H, O (octonions), S (sedenions); each step loses a property (commutativity, associativity, alternativity).
Cayley 1845 / Dickson 1919 doubling procedure: from a *-algebra A constructs a 2-dim *-algebra A x A; iterating from R produces C, H, O (octonions), S (sedenions); each step loses a property (commutativity, associativity, alternativity).