Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions
Deloro, Adrien
Confluentes Mathematici, Tome 5 (2013), p. 23-41 / Harvested from Numdam
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We classify quadratic SL 2 (𝕂)- and 𝔰𝔩 2 (𝕂)-modules by crude computation, generalising in the first case a Theorem proved independently by F.G. Timmesfeld and S. Smith. The paper is the first of a series dealing with linearisation results for abstract modules of algebraic groups and associated Lie rings.

Publié le : 2013-01-01
DOI : https://doi.org/10.5802/cml.6
Classification:  20G05,  20G15,  17B10,  17B45 
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     title = {Ver\"anderungen \"uber einen Satz von Timmesfeld -- I. Quadratic Actions},
     journal = {Confluentes Mathematici},
     volume = {5},
     year = {2013},
     pages = {23-41},
     doi = {10.5802/cml.6},
     mrnumber = {3145031},
     language = {en},
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Deloro, Adrien. Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions. Confluentes Mathematici, Tome 5 (2013) pp. 23-41. doi : 10.5802/cml.6. http://gdmltest.u-ga.fr/item/CML_2013__5_2_23_0/

[1] Chermak, Andrew Quadratic pairs, J. Algebra, Tome 277 (2004) no. 1, pp. 36-72 | Article | MR 2059620 | Zbl 1057.20001

[2] Glauberman, George A sufficient condition for p stability, Proc. London Math. Soc. (3), Tome 25 (1972), pp. 253-287 | MR 313383 | Zbl 0242.20018

[3] Ho, Chat-Yin On the quadratic pairs, J. Algebra, Tome 43 (1976) no. 1, pp. 338-358 | MR 422404 | Zbl 0385.20006

[4] Premet, Alexander Arcadievitch; Suprunenko, Irina Dmitrievna Quadratic modules for Chevalley groups over fields of odd characteristics, Math. Nachr., Tome 110 (1983), pp. 65-96 | Article | MR 721267 | Zbl 0522.20027

[5] Smith, Stephen D. Quadratic action and the natural module for SL 2 (k), J. Algebra, Tome 127 (1989) no. 1, pp. 155-162 | MR 1029409 | Zbl 0688.20023

[6] Thompson, John G. Quadratic pairs, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1, Gauthier-Villars, Paris (1971), p. 375-376 | MR 430043 | Zbl 0236.20024

[7] Timmesfeld, Franz Georg Groups generated by k-transvections, Invent. Math., Tome 100 (1990) no. 1, pp. 167-206 | MR 1037146 | Zbl 0697.20018

[8] Timmesfeld, Franz Georg Abstract root subgroups and quadratic action, Adv. Math., Tome 142 (1999) no. 1, pp. 1-150 (With an appendix by A. E. Zalesskii) | Article | MR 1671440 | Zbl 0934.20025

[9] Timmesfeld, Franz Georg Abstract root subgroups and simple groups of Lie type, Birkhäuser Verlag, Basel, Monographs in Mathematics, Tome 95 (2001) | MR 1852057 | Zbl 0984.20019