Octonions

I hope Eva and Clifford are right, but in case SUSY is essential there must be a deeper way to understand it, perhaps afforded by octonions. ❋ Sean (2006)

But there are close relationships between the representation theory of SO (8) - the transverse directions in 9+1 dim spacetime and the octonions that allow a supersymmetric theory to be defined. ❋ Sean (2006)

There is no SL (2, O), because the octonions are non-associative. ❋ Sean (2006)

If I may, one last beautiful fact: These three representations organize themselves into components of a very beautiful algebra-which is the algebra of 3 by 3 hermitian matrices of octonions. ❋ Sean (2006)

This has to do with the division algebras: A = R (real), C (complex), Q (quaternions) and O (octonions). ❋ Sean (2006)

Moshe, yes, thanks, the connection between strings and octonions is recognized but seems a possible clue to a deeper underestanding of string theory that is not yet well explored. ❋ Sean (2006)

We also know that the octonions are not only three dimensional (four if you count the zero dimensional scalars), but that they are very curious too (we read also read Baez, you know). ❋ Mark (2005)

Doug, being a reader of Baez, mentioned octonions. ❋ Mark (2005)

We know that increasing the dimension of the integers leads to complex numbers, and then to quaternions and then to octonions. ❋ Mark (2005)

Not even otherwise natural structure constants of the octonions seem to satisfy the required mutated Jacobi identity. ❋ Unknown (2010)

The very formulae for the black hole entropy must respect and do respect the U-duality, a symmetry of the theory, so they know about various cool exceptional algebraic structures such as exceptional Lie groups, octonions, GHZ states, and hyperdeterminants. ❋ Unknown (2010)

Manogue of Oregon State University are tearing them apart and examining one of their mathematical building blocks-an eight-dimensional number system called octonions. ❋ Unknown (2010)

: An exceptional Jordan algebra, consisting of 3×3 self-adjoint matrices over the octonions. ❋ Unknown (2009)