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Xiao-Gang Wen
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What are the necessary conditions for a real number to be a cyclotomic integers?

The motivation of the question is that I try to test when a real number is not an cyclotomic integers. Or more specifically, when a positive real number is not a quantum dimension of a unitary fusion category?

We know that when $1\leq d<2$, $d$ is not a quantum dimension of a unitary fusion category if $d \neq 2\cos(\pi/n), \ n=3,4,5,\cdots$

Xiao-Gang Wen
  • 4.8k
  • 22
  • 43