gh-35387: The Fusion Ring of the Drinfeld Double of a Finite Group
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### :books: Description
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This code is very similar to the existing FusionRing class. Both
FusionRing and the new FusionDouble classes implement Fusion Rings of
Modular Tensor Categories, important in conformal field theory and
related quantum math. The FusionDouble is the fusion ring of the
Drinfeld double of a finite group. It has methods corresponding to
fusion, S-matrix, twists of simple elements, quantum dimension. An
interface is provide to the F-matrix code, but due to the fact that the
number of simple objects is fairly large even for fairly small groups,
the F-matrix code is only confirmed to work for very small group such as
Z_2 and S_3. Apart from the F-matrix code, the code works for Drinfeld
doubles of moderate size, tested for example on groups of order 16, and
the simple groups A5 and GL(3,2) of orders 60 and 168.
A prototype of this code by Wenqi Li is here:
https://github.com/enqiLi/drinfeld_doubles
Work issues:
*The code would benefit from refactoring with the existing FusionRing
code. It is proposed that we skip this since the existing code works
well.
*The Drinfeld double can be twisted by a 3-cocycle for H^3(G). This may
be implemented in a later PR.
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### :hourglass: Dependencies
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URL: https://github.com/sagemath/sage/pull/35387
Reported by: Daniel Bump
Reviewer(s): Daniel Bump, Matthias Köppe, Travis Scrimshaw
