Timeline for What is the relation between quantum symmetry and quantum groups?
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21 events
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| Jun 23, 2010 at 7:35 | comment | added | The Mathemagician | @Pavel Didn't you teach a course at MIT several years ago on mathematical methods of physics that emphasize the role of tensor products?I think the notes for that course are still available at your website. | |
| Jun 23, 2010 at 3:05 | history | edited | mathphysicist |
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| Feb 25, 2010 at 12:25 | vote | accept | Xuexing Lu | ||
| Feb 25, 2010 at 12:23 | vote | accept | Xuexing Lu | ||
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| Feb 25, 2010 at 12:23 | vote | accept | Xuexing Lu | ||
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| Feb 25, 2010 at 12:21 | vote | accept | Xuexing Lu | ||
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| Feb 25, 2010 at 12:20 | vote | accept | Xuexing Lu | ||
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| Feb 24, 2010 at 20:12 | comment | added | Kim Morrison | @James; it's not appropriate to use the comments to ask more questions. Probably best to pause and think, and write a new question following the guidelines at mathoverflow.net/howtoask. | |
| Feb 24, 2010 at 5:48 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Feb 24, 2010 at 5:39 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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| Feb 23, 2010 at 14:42 | history | edited | Xuexing Lu | CC BY-SA 2.5 |
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| Feb 23, 2010 at 14:15 | answer | added | Zoran Skoda | timeline score: 11 | |
| Feb 23, 2010 at 13:48 | answer | added | Pavel Etingof | timeline score: 17 | |
| Feb 23, 2010 at 13:25 | comment | added | Xuexing Lu | Thanks Pavel Etingof! But what is a partical ? how to difine it ? Are symmetries needed to difine particals? Should they be the irreducible representions? | |
| Feb 23, 2010 at 13:18 | comment | added | Xuexing Lu | Theo Johnson-Freyd said : the short answer is that "quantum groups" were invented in the study of quantum integrable systems. quantum integrable systems,as far as my best understand from mathmatical viewpoint,are just algbras of observables with sufficent symmetries and the hilbert space of states is the module of algbra of observables. My questions are: 1 Are algbras of observables quantum groups? 2 What are the symmetry of these systems? the symmetry of algebra of observables or the symmetry of the module ? 3 What is the relation between symmetry and quantum group? | |
| Feb 23, 2010 at 13:13 | comment | added | Pavel Etingof | Tensor product is very natural in quantum mechanics since the space of quantum states of a pair of particles is the tensor product of their spaces of states (this is one of the main principles of mathematical modeling of quantum mechanics). This is how tensor products of representations arise in physics. | |
| Feb 23, 2010 at 12:47 | comment | added | Xuexing Lu | I know that quantum groups are just hopf algebtras which are bialgebras with antipode and some compatible conditions and coproducts are essential to define tensor product of modules so that the moudle category become a tensor category. But I don't know how to interpret tensor product in physical language. | |
| Feb 22, 2010 at 16:21 | comment | added | Theo Johnson-Freyd | To follow up on what GZ said: this question has the potential to become a good question, if it's dramatically expanded and motivated. As it is, it's not great. The short answer is that "quantum groups" were invented in the study of quantum integrable systems; they play the role there that Lie groups play in the theory of integrable systems. | |
| Feb 22, 2010 at 5:54 | comment | added | Gjergji Zaimi | It wouldn't hurt your chances for a better answer if you included some motivation to asking this question/ what have you read so far etc. In my opinion the question as stated now is vague enough to only admit an encyclopedic answer (i.e. nothing you wouldn't find on Wiki). | |
| Feb 22, 2010 at 3:44 | comment | added | B. Bischof | You might be interested in the question over here: mathoverflow.net/questions/14680/… | |
| Feb 22, 2010 at 3:07 | history | asked | Xuexing Lu | CC BY-SA 2.5 |