Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Gerhard P. Hochschild
Title: Basic theory of algebraic groups and Lie algebras
Additional book information: Graduate Texts in Mathematics, vol. 75, Springer-Verlag, New York, Heidelberg, Berlin, 1981, viii + 267 pp., $32.00. ISBN 0-3879-0541-3.

Author: T. A. Springer
Title: Linear algebraic groups
Additional book information: Progress in Mathematics, vol. 9, Birkhauser, Boston; Basel, Stuttgart, 1981, x + 304 pp., $20.00. ISBN 3-7643-2039-5.

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

  • 1. Armand Borel, Groupes linéaires algébriques, Ann. of Math. (2) 64 (1956), 20–82 (French). MR 0093006, https://doi.org/10.2307/1969949
  • 2. Armand Borel, Linear algebraic groups, Notes taken by Hyman Bass, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0251042
  • 3. A. Borel, On the development of Lie group theory, Math. Intelligencer 2 (1979/80), no. 2, 67–72. L. E. J. Brouwer Memorial Lecture. MR 577554, https://doi.org/10.1007/BF03023375
  • 4. Roger W. Carter, Simple groups of Lie type, John Wiley & Sons, London-New York-Sydney, 1972. Pure and Applied Mathematics, Vol. 28. MR 0407163
  • 5. C. Chevalley, Séminaire sur la classification des groupes de Lie algébriques, École Norm. Sup., Paris, 1956-1958.
  • 6. C. Chevalley, Sur certains groupes simples, Tôhoku Math. J. (2) 7 (1955), 14–66 (French). MR 0073602, https://doi.org/10.2748/tmj/1178245104
  • 7. Claude Chevalley, Théorie des groupes de Lie. Tome II. Groupes algébriques, Actualités Sci. Ind. no. 1152, Hermann & Cie., Paris, 1951 (French). MR 0051242
  • 8. Schémas en groupes. I: Propriétés générales des schémas en groupes, Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3). Dirigé par M. Demazure et A. Grothendieck. Lecture Notes in Mathematics, Vol. 151, Springer-Verlag, Berlin-New York, 1970 (French). MR 0274458
    Schémas en groupes. II: Groupes de type multiplicatif, et structure des schémas en groupes généraux, Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3). Dirigé par M. Demazure et A. Grothendieck. Lecture Notes in Mathematics, Vol. 152, Springer-Verlag, Berlin-New York, 1970 (French). MR 0274459
    Schémas en groupes. III: Structure des schémas en groupes réductifs, Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3). Dirigé par M. Demazure et A. Grothendieck. Lecture Notes in Mathematics, Vol. 153, Springer-Verlag, Berlin-New York, 1970 (French). MR 0274460
  • 9. I. B. Frenkel and V. G. Kac, Basic representations of affine Lie algebras and dual resonance models, Invent. Math. 62 (1980/81), no. 1, 23–66. MR 595581, https://doi.org/10.1007/BF01391662
  • 10. G. Hochschild, Algebraic Lie algebras and representative functions, Illinois J. Math. 3 (1959), 499–523. MR 0125910
  • 11. G. Hochschild, The structure of Lie groups, Holden-Day, Inc., San Francisco-London-Amsterdam, 1965. MR 0207883
  • 12. James E. Humphreys, Linear algebraic groups, Springer-Verlag, New York-Heidelberg, 1975. Graduate Texts in Mathematics, No. 21. MR 0396773
  • 13. E. R. Kolchin, Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations, Ann. of Math. (2) 49 (1948), 1–42. MR 0024884, https://doi.org/10.2307/1969111
  • 14. G. D. Mostow, Fully reducible subgroups of algebraic groups, Amer. J. Math. 78 (1956), 200–221. MR 0092928, https://doi.org/10.2307/2372490

Review Information:

Reviewer: Brian Parshall
Journal: Bull. Amer. Math. Soc. 9 (1983), 364-368
DOI: https://doi.org/10.1090/S0273-0979-1983-15212-6