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In mathematics and physics, an anyon is a type of projective representation of a Lie group.
In detail, there are projective representations of SO(2,1) which don't arise from linear representations of SO(2,1), or of its double cover, Spin(2,1). These representations are called anyons.
The topological reason behind the phenomenon is this: the first homotopy group of SO(2,1) (and also Poincaré(2,1)) is Z (infinite cyclic). This means that Spin(2,1) is not the universal cover: it is not simply connected. On the other hand, for n > 2, for SO(n,1) and Poincaré(n,1), it's only Z2 (cyclic of order 2); meaning that the spin group is simply connected.
See also: plekton.
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