Hypercomplex algebras are formed by doubling previously formed algebras.
For example, the Cayley-Dickson construction, (a,b)(c,d)=(ac-bd,ad-bc), forms
the sequence of algebras real, complex, quaternion, octonion, sedenion.

### Hierarchy of hypergeometric algebras

. . . . . . the following outline structure might be better represented
as a picture (although we should leave the outline structure here, and explain
how to derive each algebra from its predecessor).

Reals

Complex

Quaternion

Octonion

Sedenion

Split-quaternion

Split-complex

Double

Dual

### Cayley-Dickson construction

. . . . . .

### Kronecker product construction

. . . . . .

### Division algebra

. . . . . . A division algebra is . . . . . .

### Clifford algebras

. . . . . . related to division algebras

### Internet references

Euclidean Space:
hypercomplex

### Related pages in this website

Complex,
Quaternion,
Octonion, and
Sedenion numbers are n-tuples of
real numbers, where n=2,4,8,16, respectively.

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Graeme McRae.