Timeline for Hopf algebra of Chevalley group from the root system
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 14, 2011 at 13:27 | vote | accept | Baptiste Calmès | ||
| Jul 14, 2011 at 13:26 | comment | added | Baptiste Calmès | I'm accepting this answer (especially the paper cited by Jim Humphrey in his comment), because it seems to reflect the best available in the literature in the spirit of what I was asking, but I wish the description was simpler: I do not understand very well the constants involved, they look very complicated to me, and I wish there was a more "invariant" description. It might be because I'm not very familiar with universal enveloping algebras, and their quantized versions. | |
| May 19, 2011 at 18:08 | comment | added | Victor Petrov | By the way, the paper of Kostant himself is short and useful ("Groups over Z", in Algebraic groups and discontinuos subgroups, 1966). | |
| May 18, 2011 at 20:32 | comment | added | Jim Humphreys | P.S. Preprint versions of the two papers by Lusztig mentioned here are on arXiv, while Chevalley's Bourbaki talk is available online at www.numdam.org. Also, Takeuchi's approach is treated in Jantzen's book Representations of Algebraic Groups, in II.1.14, though that may not be so relevant to your question | |
| May 18, 2011 at 19:18 | comment | added | Baptiste Calmès | Thanks for both of these references. At first sight, they seem to be what I am looking for, although I need to work through the notation and the notions to be really sure. | |
| May 18, 2011 at 18:09 | comment | added | Jim Humphreys | Lusztig's work improves (and in some ways corrects) what Chevalley did earlier while completing the program in Kostant's 1965 AMS Summer Institute paper. The full details are in a paper not linked from his home page: Study of a Z-form of the coordinate ring of a reductive group, J.Amer.Math.Soc. 22(2009), 739-769. | |
| May 18, 2011 at 15:37 | history | answered | Marty | CC BY-SA 3.0 |