Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions
Confluentes Mathematici, Volume 5 (2013) no. 2, pp. 25-46.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/cml.6
Classification: 20G05,  20G15,  17B10,  17B45
Adrien Deloro 1

1 Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4, place Jussieu, 75005 Paris, France
@article{CML_2013__5_2_25_0,
     author = {Adrien Deloro},
     title = {Ver\"anderungen \"uber einen {Satz} von {Timmesfeld} {\textendash} {I.} {Quadratic} {Actions}},
     journal = {Confluentes Mathematici},
     pages = {25--46},
     publisher = {Institut Camille Jordan},
     volume = {5},
     number = {2},
     year = {2013},
     doi = {10.5802/cml.6},
     language = {en},
     url = {https://cml.centre-mersenne.org/articles/10.5802/cml.6/}
}
TY  - JOUR
AU  - Adrien Deloro
TI  - Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions
JO  - Confluentes Mathematici
PY  - 2013
DA  - 2013///
SP  - 25
EP  - 46
VL  - 5
IS  - 2
PB  - Institut Camille Jordan
UR  - https://cml.centre-mersenne.org/articles/10.5802/cml.6/
UR  - https://doi.org/10.5802/cml.6
DO  - 10.5802/cml.6
LA  - en
ID  - CML_2013__5_2_25_0
ER  - 
%0 Journal Article
%A Adrien Deloro
%T Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions
%J Confluentes Mathematici
%D 2013
%P 25-46
%V 5
%N 2
%I Institut Camille Jordan
%U https://doi.org/10.5802/cml.6
%R 10.5802/cml.6
%G en
%F CML_2013__5_2_25_0
Adrien Deloro. Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions. Confluentes Mathematici, Volume 5 (2013) no. 2, pp. 25-46. doi : 10.5802/cml.6. https://cml.centre-mersenne.org/articles/10.5802/cml.6/

[1] Andrew Chermak Quadratic pairs, J. Algebra, Volume 277 (2004) no. 1, pp. 36-72 | DOI

[2] George Glauberman A sufficient condition for p stability, Proc. London Math. Soc. (3), Volume 25 (1972), pp. 253-287

[3] Chat-Yin Ho On the quadratic pairs, J. Algebra, Volume 43 (1976) no. 1, pp. 338-358

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

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

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

[7] Franz Georg Timmesfeld Groups generated by k-transvections, Invent. Math., Volume 100 (1990) no. 1, pp. 167-206

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

[9] Franz Georg Timmesfeld Abstract root subgroups and simple groups of Lie type, Monographs in Mathematics, 95, Birkhäuser Verlag, Basel, 2001, xiv+389 pages

Cited by Sources: