Journal of Symbolic Logic

Small representations of SL2 in the finite Morley rank category

Gregory Cherlin and Adrien Deloro

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We study definable irreducible actions of SL2(𝕂) on an abelian group of Morley rank ≤ 3rk(𝕂) and prove they are rational representations of the group.

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J. Symbolic Logic Volume 77, Issue 3 (2012), 919-933.

First available in Project Euclid: 13 August 2012

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Cherlin, Gregory; Deloro, Adrien. Small representations of SL 2 in the finite Morley rank category. J. Symbolic Logic 77 (2012), no. 3, 919--933. doi:10.2178/jsl/1344862167.

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  • A. Baudisch, A. Martin-Pizarro, and M. Ziegler Red fields, Journal of Symbolic Logic, vol. 72(2007), no. 1, pp. 207–225.
  • Armand Borel and Jacques Tits Groupes réductifs, Publications Mathématiques. Institut de Hautes Études Scientifiques, vol. 27(1965), pp. 55–151.
  • –––– Homomorphismes “abstraits” de groupes algébriques simples, Annals of Mathematics. Second Series, vol. 97(1973), pp. 499–571.
  • Alexandre Borovik and Ali Nesin Groups of finite Morley rank, Oxford Logic Guides, vol. 26, The Clarendon Press – Oxford University Press, New York,1994.
  • Gregory Cherlin Good tori in groups of finite Morley rank, Journal of Group Theory, vol. 8(2005), no. 5, pp. 613–621.
  • Adrien Deloro Actions of groups of finite Morley rank on small abelian groups, Bulletin of Symbolic Logic, vol. 15(2009), no. 1, pp. 70–90.
  • James G. Loveys and Frank O. Wagner Le Canada semi-dry, Proceedings of the American Mathematical Society, vol. 118(1993), no. 1, pp. 217–221.
  • Dugald Macpherson and Anand Pillay Primitive permutation groups of finite Morley rank, Proceedings of the London Mathematical Society. Third Series, vol. 70(1995), no. 3, pp. 481–504.
  • Bruno Poizat Groupes stables, Nur al-Mantiq wal-Ma'rifah, Villeurbanne,1987.
  • –––– Quelques modestes remarques à propos d'une conséquence inattendue d'un résultat surprenant de Monsieur Frank Olaf Wagner, Journal of Symbolic Logic, vol. 66(2001), pp. 1637–1646.
  • Robert Steinberg Abstract homomorphisms of simple algebraic groups $($after A. Borel and J. Tits$)$, Séminaire Bourbaki, 25ème année $($1972/1973$)$, Exp. No. 435, Lecture Notes in Mathematics, vol. 383, Springer, Berlin,1974, pp. 307–326.
  • Franz Georg Timmesfeld Abstract Root Subgroups and Simple Groups of Lie-type, Monographs in Mathematics, vol. 95, Birkhäuser, Basel,2001.
  • Frank Wagner Fields of finite Morley rank, Journal of Symbolic Logic, vol. 66(2001), no. 2, pp. 703–706.