Timeline for Quantum double vs Quantum group
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 21, 2021 at 8:06 | comment | added | user160032 | @JulesLamers Yes, it might have been a hyperbole. But here are several meanings: Hopf algebra that is neither commutative/cocommutative, hopf *-algebra with integral, multiplier Hopf algebra with integrals, quasitriangular Hopf algebra, compact matrix quantum group and their more general versions compact quantum groups (in the sense of Woronowicz), locally compact quantum group (in the sense of Vaes and Kustermans), and I think the point is clear now that at least some context/direction should be specified! | |
| May 21, 2021 at 7:24 | comment | added | Jules Lamers | @zibadawatimmy Thanks. While I don't disagree, I don't know if the hyperbole is all that useful and necessarily clear to the OP given the level of the question -- whence my comment | |
| May 21, 2021 at 7:19 | comment | added | zibadawa timmy | @JulesLamers 20 is clearly just hyperbole to emphasize the point that the term is ambiguous even to what one might call an "expert on quantum groups". I've seen the terminology pop up just about any time someone constructs a generalization/substitute of a group/Hopf algebra that's somehow vaguely "quantum". To the extent that one might think that any quasi-Hopf algebra and/or its representation category is a "quantum group", or maybe only if it's quasitriangular. Here the "vaguely quantum" bit is that the representation category can now have a non-trivial associator. | |
| May 21, 2021 at 3:37 | comment | added | Jules Lamers | @MathQED While there are indeed various different meanings of 'quantum group' -- eg Drinfeld--Jimbo quantised universal enveloping (+ its Yangian limit), Felder elliptic, Woronowicz compact -- and I am willing to believe that you know a handful of them, 20 seems a lot. Please enlighten me | |
| May 21, 2021 at 0:46 | answer | added | Calvin McPhail-Snyder | timeline score: 9 | |
| May 20, 2021 at 23:11 | comment | added | Sam Hopkins | @MathQED: while I agree that in general it is good to include that kind of context, this particular question is essentially asking for definitions and references. | |
| May 20, 2021 at 23:06 | comment | added | user160032 | Please include definitions/references. The term quantum group is ambiguous. I know about 20 different uses of this terminology. | |
| May 20, 2021 at 23:06 | comment | added | Nik Weaver | Drinfel'd double | |
| May 20, 2021 at 22:50 | review | First posts | |||
| May 21, 2021 at 5:55 | |||||
| May 20, 2021 at 22:44 | history | asked | user232343 | CC BY-SA 4.0 |