4. Number theoretic questions
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Problem 4.1.
[Snyder] Is there a sense in which a randomly chosen fusion graph doesn’t have cylotomic dimensions? -
Problem 4.2.
[Snyder] Look at all spoke graphs with N>0 arms. Are there finitely many N-tuples (\ell_1,\dots, \ell_N) such that the spoke graph with N arms of lengths \ell_1,\dots, \ell_N has cyclotomic norm squared? -
Problem 4.1.
[Morrison] Is there a positive real number which is a cyclotomic integer and is largest amongst its Galois conjugates, but which is not realized as the dimension of an object in a fusion category?-
Remark. [Scott Morrison] The first five such numbers above 2, given in [arxiv:1004.0665], are all known to be realized.
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Cite this as: AimPL: Classifying fusion categories, available at http://aimpl.org/fusioncat.