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Tagged with cyclotomic-fields subfactors
3 questions
9
votes
2
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775
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How can I prove that a sequence of squares of graph norms is never cyclotomic?
The norm of a graph is the largest eigenvalue of the adjacency matrix. I'll write ||G|| for the norm of G.
Now, fix some graph <...
- 7,800
3
votes
0
answers
134
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What are all the possible indices for the finite depth subfactors?
Jones index theorem (1983) states that the set of all possible (finite) indices of subfactors is exactly $$\mathrm{Ind}=\{ 4 \cos(\pi/n)^2 \ | \ n \ge 3 \} \cup [4, \infty),$$ but if we restrict to ...
2
votes
0
answers
156
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Extension of a theorem of Bisch to cyclotomic integers of fixed degree
Theorem 3.2 in this paper (Bisch, 1994) states that for a finite depth ${\rm II}_1$ subfactor of integral index, every intermediate subfactor are also of integral index. As an application, every such ...