Timeline for Classical (i.e. commutative) spaces with quantum symmetry but no classical symmetry
Current License: CC BY-SA 4.0
10 events
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| Mar 5 at 15:06 | comment | added | J. van Dobben de Bruyn | @SebastienPalcoux in addition to the "(not so) brief description" which David added to the question, you can also take a look at these slides, which give a high-level outline of the proof (from slide 10 onwards). Though I guess some parts of the talk, including the description of the graph, might require some verbal explanation, which is not part of the slides. 😅 | |
| Mar 5 at 11:53 | history | edited | David Roberson | CC BY-SA 4.0 |
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| Mar 5 at 10:45 | comment | added | David Roberson | @SebastienPalcoux 5880 edges. The only method I can think of for getting such a lower bound is to check all asymmetric graphs on few vertices and show they have no quantum symmetry. There are too many of these so instead you should check asymmetric coherent configurations, which would suffice. There are only 9839 coherent configurations on 15 points (actamath.savbb.sk/pdf/aumb2605.pdf), so this is probably doable. I expect none are asymmetric but with quantum symmetry. Not a great lower bound and I would guess checking for q-symmetry in general is undecidable, so not a great approach. | |
| Mar 5 at 9:58 | comment | added | Sebastien Palcoux | A challenge would be to identify increasingly smaller graphs of this type. What is the lowest bound you can determine for the number of edges (or vertices)? | |
| Mar 5 at 9:42 | comment | added | Sebastien Palcoux | I see. You mentioned 560 vertices; how many edges does that entail? I presume there's software designed for efficiently visualizing such large graphs, possibly used in big data fields. Regardless, a concise explanation would indeed be appreciated! | |
| Mar 5 at 9:10 | comment | added | David Roberson | @SebastienPalcoux I'd love it if such an image could be made that wouldn't be incomprehensible, but even if I am allowed edge and vertex colors, the smallest such graph we construct would have 560 vertices. So I think the image would just end up being a big blob. I can give a brief description if you'd like. | |
| Mar 5 at 8:50 | comment | added | Sebastien Palcoux | Fascinating! Could you please include an image of the simplest graph that possesses this property? | |
| Mar 5 at 8:40 | comment | added | JP McCarthy | Another avenue to look at (and again not answering the question - the answer as far as I understand is no, no known examples.): mathoverflow.net/questions/188707/… | |
| Mar 5 at 7:21 | comment | added | JP McCarthy | Probably worth noting that for connected manifolds the usual situation is that there are classical symmetries but no genuine symmetries. Cf work of Goswami. Freslon and Goswami would be people to possibly email this question to. | |
| Mar 4 at 23:31 | history | asked | David Roberson | CC BY-SA 4.0 |