Bott-Milnor-Kervaire 1,2,4,8 Theorem

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Theorem

Let $A$ be a division algebra with real scalars.


Then the dimension of $A$ is either:

$1$: the real numbers $\R$
$2$: the complex numbers $\C$
$4$: the quaternions $\Bbb H$

or:

$8$: the octonions $\Bbb O$.


Proof


Source of Name

This entry was named for Raoul Bott, John Willard Milnor and Michel André Kervaire.


Historical Note

Bott-Milnor-Kervaire 1,2,4,8 Theorem was proved by Raoul Bott, John Willard Milnor and Michel André Kervaire in $1958$.


Sources