A222011 Dimensions of finite-dimensional real division algebras.

1, 2, 4, 8

Offset

0,2

Comments

In 1958 Michel Kervaire and John Milnor independently proved that any finite-dimensional 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