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Automorphisms of $ {\rm SL}\sb 2$ of imaginary quadratic integers


Authors: John Smillie and Karen Vogtmann
Journal: Proc. Amer. Math. Soc. 112 (1991), 691-699
MSC: Primary 20G30; Secondary 11E57, 20F28
DOI: https://doi.org/10.1090/S0002-9939-1991-1065094-6
MathSciNet review: 1065094
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Abstract: We determine the outer automorphism groups of the two-dimensional special linear and projective special linear groups of the ring of integers in an imaginary quadratic field.


References [Enhancements On Off] (What's this?)

  • [1] L. Bianchi, Sui gruppi di sostituzioni lineari con coefficienti appartenenti a corpi quadratici immaginari, Math. Ann. 40 (1894), 332-412. MR 1510727
  • [2] A. Chatelet, L'arithmetique des corps quadriques, Monographies de L'Enseignement Mathematique, no. 9, Institute de Mathematiques, Universite Geneve, 1962. MR 0172863 (30:3080)
  • [3] J. E. Cremona, On $ GL\left( n \right)$ of a Dedekind domain, Quart. J. Math. Oxford, Ser. 2 39 (1988), 423-426. MR 975907 (89k:20061)
  • [4] M. Dull, Automorphisms of $ PS{L_2}$ over domains with few units, J. Algebra 27 (1973), 372-379. MR 0327924 (48:6266)
  • [5] -, Automorphisms of the two-dimensional linear groups over integral domains, Amer. J. Math. 96 (1974), 1-40. MR 0357638 (50:10106)
  • [6] C S. Herz, Construction of class fields, Seminar on complex multiplication, Lecture Notes in Math., vol. 21, Springer-Verlag, New York, 1966.
  • [7] E. Mendoza, Cohomology of $ PG{L_2}$ over imaginary quadratic integers, Thesis, Bonn, 1979. MR 611515 (82g:22012)
  • [8] J. Milnor, Introduction to algebraic $ K$-theory, Ann. Math. Stud., Princeton Univ. Press, Princeton, NJ, 1971. MR 0349811 (50:2304)
  • [9] G. Mostow, Strong rigidity of locally symmetric spaces, Princeton Univ. Press, Princeton, NJ, 1973. MR 0385004 (52:5874)
  • [10] O. T. O'Meara, Lectures on linear groups, Regional Conference Series in Mathematics, no. 22, Amer. Math. Soc., Providence, RI, 1974. MR 0349862 (50:2355)
  • [11] J. Schweriner and K. Vogtmann, Integral cohomology of $ S{L_2}$ of Euclidean imaginary quadratic integers, Comment. Math. Helv. 58 (1983), 573-598. MR 728453 (86d:11046)
  • [12] K. Vogtmann, Rational homology of Bianchi groups, Math. Ann. 272 (1985), 399-419. MR 799670 (87a:22025)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1065094-6
Article copyright: © Copyright 1991 American Mathematical Society

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