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Book Review

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Book Information:

Author: George B. Seligman
Title: Rational methods in Lie algebras
Additional book information: Lecture Notes in Pure and Applied Math., vol. 17, Marcel Dekker, New York and Basel, 1976, viii + 346 pp., $29.50.

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

  • 1. B. N. Allison, Isomorphism of simple Lie algebras, Trans. Amer. Math. Soc. 177 (1973), 173–190. MR 0327852, https://doi.org/10.1090/S0002-9947-1973-0327852-6
  • 2. Shôrô Araki, On root systems and an infinitesimal classification of irreducible symmetric spaces, J. Math. Osaka City Univ. 13 (1962), 1–34. MR 0153782
  • 3. Armand Borel and Jacques Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55–150 (French). MR 0207712
  • 4. Elie Cartan, Les groupes réels simples, finis et continus, Ann. Sci. École Norm. Sup. (3) 31 (1914), 263–355 (French). MR 1509178
  • 5. Felix Gantmacher, On the classification of real simple Lie groups, Rec. Math. [Mat. Sbornik] N.S. 5 (47) (1939), 217–250 (English, with Russian summary). MR 0002141
  • 6. Nathan Jacobson, Rational methods in the theory of Lie algebras, Ann. of Math. (2) 36 (1935), no. 4, 875–881. MR 1503258, https://doi.org/10.2307/1968593
  • 7. Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. MR 0143793
  • 8. W. Landherr, Über einfache Liesche Ringe, Abh. Math. Sem. Univ. Hamburg 11 (1935), 41-64.
  • 9. W. Landherr, Liesche Ringe vom Typus A über einem algebraischen Zahlkörper (Die lineare Gruppe) und hermitesche Formen über einem Schiefkörper, Abh. Math. Sem. Univ. Hamburg 12 (1938), 200-241.
  • 10. Shingo Murakami, Sur la classification des algèbres de Lie réelles et simples, Osaka J. Math. 2 (1965), 291–307 (French). MR 0201578
  • 11. I. Satake, Classification theory of semi-simple algebraic groups, Marcel Dekker, Inc., New York, 1971. With an appendix by M. Sugiura; Notes prepared by Doris Schattschneider; Lecture Notes in Pure and Applied Mathematics, 3. MR 0316588
  • 12. Martin Selbach, Klassifikationstheorie halbeinfacher algebraischer Gruppen, Mathematisches Institut der Universität Bonn, Bonn, 1976. Diplomarbeit, Univ. Bonn, Bonn, 1973; Bonner Mathematische Schriften, Nr. 83. MR 0432776
  • 13. J. Tits, Une classe d’algèbres de Lie en relation avec les algèbres de Jordan, Nederl. Akad. Wetensch. Proc. Ser. A 65 = Indag. Math. 24 (1962), 530–535 (French). MR 0146231
  • 14. J. Tits, Classification of algebraic semisimple groups, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, 1966, pp. 33–62. MR 0224710

Review Information:

Reviewer: J. E. Humphreys
Journal: Bull. Amer. Math. Soc. 83 (1977), 993-997
DOI: https://doi.org/10.1090/S0002-9904-1977-14348-6