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Book Review
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Book Information
Author(s):
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(s):
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:
- 1.
- A. Borel, Groupes linéaires algébriques, Ann. of Math. (2) 64 (1956), 20-80. MR 93006
- 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
Additional Information:
Reviewer(s):
Brian
Parshall
Review Information:
Journal:
Bull. Amer. Math. Soc.
9
(1983),
364-368.
DOI:
10.1090/S0273-0979-1983-15212-6
PII:
S 0273-0979(1983)15212-6
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