Timeline for Lie bialgebras cohomology
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 18, 2014 at 9:44 | comment | added | Nicola Ciccoli | A very down to earth approach connecting to deformation theory is in my joint paper with L. Guerra "The variety of Lie bialgebras" emis.de/journals/JLT/vol.13_no.2/16.html | |
| Nov 28, 2014 at 21:22 | comment | added | Theo Johnson-Freyd | I agree with Gabriel's comments, but want to add one remark. There are different ways to model many-to-many operations: properads and props (which are essentially equivalent, by a deep result of Vallette's) allow compositions of arbitrary "genus" (or "loop order"); an alternate version, called "dioperads", uses only "tree-level" compositions. This in general makes a huge difference: the answers to homological-type questions can be very difference. I think that for Lie bialgebras, you happen to get the same answers in the different settings, but for other types of bialgebras you often do not. | |
| Nov 28, 2014 at 11:51 | comment | added | Gabriel C. Drummond-Cole | I believe that the case of Lie bialgebras was worked out earlier by hand in Y. Kosmann-Schwarzbach, Grand crochet, crochets de Schouten et cohomologies d’algèbres de Lie, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 1, 123–126., but I haven't actually read it. | |
| Nov 28, 2014 at 11:43 | comment | added | Gabriel C. Drummond-Cole | You should go to properads if you want to model bialgebras. A general theory that suffices for bialgebras is worked out in "Deformation theory of representations of prop(erad)s I and II" by Merkulov and Vallette. | |
| Nov 28, 2014 at 11:11 | history | asked | user56980 | CC BY-SA 3.0 |