

A222011


Dimensions of finitedimensional real division algebras.


1




OFFSET

0,2


COMMENTS

In 1958 Michel Kervaire and John Milnor independently proved that any finitedimensional real division algebra must be of dimension 1, 2, 4, or 8.


LINKS

Table of n, a(n) for n=0..3.
Wikipedia, Division algebra


FORMULA

a(n) = 2^n = A222010(n) + 1 for n = 0, 1, 2, 3.


EXAMPLE

The real, complex, quaternion, and Cayley numbers are real division algebras of dimensions 1, 2, 4, 8, respectively, so those are members.


CROSSREFS

Cf. A222010.
Sequence in context: A103009 A174393 A153662 * A063864 A186036 A186040
Adjacent sequences: A222008 A222009 A222010 * A222012 A222013 A222014


KEYWORD

nonn,fini,full


AUTHOR

Jonathan Sondow, Feb 06 2013


STATUS

approved



