So I have an interest in hypercomplex numbers and Clifford Algebras and was wondering a few months ago about other hypercomplex numbers besides the celebrated Quaternions and Octonions. I tried to construct a 5D complex number system using a Cayley table but noticed that entries in rows and columns were redundant. But what about a 6D complex number system? Well I managed to come up with a proposal using a Cayley table(and I do not claim to be the true originator) and here it is:(adsbygoogle = window.adsbygoogle || []).push({});

Now the rule to generate this Cayley table isi=^{2}j^{2}=k^{2}=l^{2}=r^{2}=-1

Andijklr = (ij)(kl)r = -1

Now this is a non-associative algebra because (for example)

i((jk)(lr))= i(-rk) = i=^{2}-1

and(i(jk)(lr) = jk = -r

Has anyone else seen an Algebra like this before? I googled "sextenions" and found one article from 11 years ago where it mentioned a 6D complex number system but did not present a Cayley multiplication table for it.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Sextenions (6D hypercomplex numbers)

Tags:

Loading...

Similar Threads for Sextenions hypercomplex numbers |
---|

A Last Gauss Lemma Section II |

B Why does every subfield of Complex number have a copy of Q? |

**Physics Forums | Science Articles, Homework Help, Discussion**