In 1996, C. Nayak and Frank Wilczek posited that in analogy to projective representations of SO(3), the projective representations of the braid group have a physical meaning for certain quasiparticles in the fractional quantum hall effect.
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He found one of the first applications of large cardinals to algebra by constructing a certain left-invariant total order, called the Dehornoy order, on the braid group.