... C , we can then write A = B ⊕ C, the direct sum of B and C as algebras As in the case of vector spaces, the notion of direct sum extends to an arbitrary (indexed) set of summands In these notes ... We begin by returning to the Peirce decomposition (10) of any Jordan algebra J relative to an idempotent e The subspaces J1 and J0 are orthogonal subalgebras of J which are related to the subspace ... each row of the formula (4m) we have left one of the four elements x, y, z, w fixed in the middle position of the associator and permuted the remaining three cyclically We omit the proof of the fact...