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Bulletin of the American Mathematical Society

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

Book Review

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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?)

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  • 2. A. Borel, Linear algebraic groups, Benjamin, New York, 1969. MR 251042
  • 3. A. Borel, On the development of Lie group theory, Math. Intelligencer 2 (1980), 67-72. MR 577554
  • 4. R. Carter, Simple groups of Lie type, Wiley, London and New York, 1972. MR 407163
  • 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. 7 (1955), 14-66. MR 73602
  • 7. C. Chevalley, Théorie des groupes de Lie. Tome II, Groupes algébriques (1951); Tome III, Théorèmes généraux sur les algèbres de Lie. (1955), Hermann, Paris. MR 51242
  • 8. M. Demazure and A. Grothendieck, Schémas en groupes, Lecture Notes in Math., vols. 151, 152, 155, Springer-Verlag, Berlin and New York, 1970. MR 274458
  • 9. I. Frenkel and V. Kac, Basic representations of affine Lie algebras and dual resonance models, Invent. Math. 62 (1980), 23-66. MR 595581
  • 10. G. Hochschild, Algebraic Lie algebras and representative functions, Illinois J. Math. 3 (1959), 499-523; supplement, ibid. 4 (1960), 609-618. MR 125910
  • 11. G. Hochschild, The structure of Lie groups, Holden-Day, San Francisco, 1965. MR 207883
  • 12. J. Humphreys, Linear algebraic groups, Springer-Verlag, Berlin and New York, 1975. MR 396773
  • 13. E. Kolchin, Algebraic matrix groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations, Ann. of Math. (2) 49 (1948), 1-42. MR 24884
  • 14. G. Mostow, Fully reducible subgroups of algebraic groups, Amer. J. Math. 78 (1956), 200-221. MR 92928

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
American Mathematical Society