Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. Plural form of octonion.

Etymologies

Sorry, no etymologies found.

Examples

  • 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.

    Why 10 or 11?

  • 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.

    Why 10 or 11?

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

    Why 10 or 11?

  • 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.

    Why 10 or 11?

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

    Why 10 or 11?

  • 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.

    Why 10 or 11?

  • 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).

    Our First Guest Blogger - Lawrence Krauss

  • Doug, being a reader of Baez, mentioned octonions.

    Our First Guest Blogger - Lawrence Krauss

  • We know that increasing the dimension of the integers leads to complex numbers, and then to quaternions and then to octonions.

    Our First Guest Blogger - Lawrence Krauss

  • Not even otherwise natural structure constants of the octonions seem to satisfy the required mutated Jacobi identity.

    The Reference Frame

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