Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions

Adrien Deloro[1]

  • [1] Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4, place Jussieu, 75005 Paris, France

Confluentes Mathematici (2013)

  • Volume: 5, Issue: 2, page 23-41
  • ISSN: 1793-7434

Abstract

top
We classify quadratic - and -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.

How to cite

top

Deloro, Adrien. "Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions." Confluentes Mathematici 5.2 (2013): 23-41. <http://eudml.org/doc/275476>.

@article{Deloro2013,
abstract = {We classify quadratic $\operatorname\{SL\}_2(\mathbb\{K\})$- and $\mathfrak\{sl\}_2(\mathbb\{K\})$-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.},
affiliation = {Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4, place Jussieu, 75005 Paris, France},
author = {Deloro, Adrien},
journal = {Confluentes Mathematici},
keywords = {quadratic modules; modules of algebraic groups; associated Lie rings},
language = {eng},
number = {2},
pages = {23-41},
publisher = {Institut Camille Jordan},
title = {Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions},
url = {http://eudml.org/doc/275476},
volume = {5},
year = {2013},
}

TY - JOUR
AU - Deloro, Adrien
TI - Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions
JO - Confluentes Mathematici
PY - 2013
PB - Institut Camille Jordan
VL - 5
IS - 2
SP - 23
EP - 41
AB - We classify quadratic $\operatorname{SL}_2(\mathbb{K})$- and $\mathfrak{sl}_2(\mathbb{K})$-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.
LA - eng
KW - quadratic modules; modules of algebraic groups; associated Lie rings
UR - http://eudml.org/doc/275476
ER -

References

top
  1. Andrew Chermak, Quadratic pairs, J. Algebra 277 (2004), 36-72 Zbl1057.20001MR2059620
  2. George Glauberman, A sufficient condition for stability, Proc. London Math. Soc. (3) 25 (1972), 253-287 Zbl0242.20018MR313383
  3. Chat-Yin Ho, On the quadratic pairs, J. Algebra 43 (1976), 338-358 Zbl0385.20006MR422404
  4. Alexander Arcadievitch Premet, Irina Dmitrievna Suprunenko, Quadratic modules for Chevalley groups over fields of odd characteristics, Math. Nachr. 110 (1983), 65-96 Zbl0522.20027MR721267
  5. Stephen D. Smith, Quadratic action and the natural module for , J. Algebra 127 (1989), 155-162 Zbl0688.20023MR1029409
  6. John G. Thompson, Quadratic pairs, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1 (1971), 375-376, Gauthier-Villars, Paris Zbl0236.20024MR430043
  7. Franz Georg Timmesfeld, Groups generated by -transvections, Invent. Math. 100 (1990), 167-206 Zbl0697.20018MR1037146
  8. Franz Georg Timmesfeld, Abstract root subgroups and quadratic action, Adv. Math. 142 (1999), 1-150 Zbl0934.20025MR1671440
  9. Franz Georg Timmesfeld, Abstract root subgroups and simple groups of Lie type, 95 (2001), Birkhäuser Verlag, Basel Zbl0984.20019MR1852057

NotesEmbed ?

top

You must be logged in to post comments.