Spinor Group
In
mathematics
the
spinor group
Spin(
n
) is a particular
double cover
of the
special orthogonal group
SO(
n
,
R
). That is, there exists a
short exact sequence
of
Lie groups
1\to\mathbb{Z}_2\to\operatorname{Spin}(n)\to\operatorname{SO}(n)\to 1
For
n
> 2, Spin(
n
) is
simply connected
and so coincides with the
universal cover
of SO(
n
,
R
). As a Lie group Spin(
n
) therefore shares its dimension
n(n-1)/2
and its
Lie algebra
with the special orthogonal group. Spin(
n
) can be constructed as a
subgroup
of the invertible elements in the
Clifford algebra
C
(
n
).
See also
:
spinor
,
spinor bundle
,
anyon
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