Bulletin of the American Mathematical Society

MathSciNet review: 1566997
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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.

B. N. Allison, Isomorphism of simple Lie algebras, Trans. Amer. Math. Soc. 177 (1973), 173–190. MR 327852, DOI 10.1090/S0002-9947-1973-0327852-6

Shôrô Araki, On root systems and an infinitesimal classification of irreducible symmetric spaces, J. Math. Osaka City Univ. 13 (1962), 1–34. MR 153782

Armand Borel and Jacques Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55–150 (French). MR 207712

Elie Cartan, Les groupes réels simples, finis et continus, Ann. Sci. École Norm. Sup. (3) 31 (1914), 263–355 (French). MR 1509178

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

Nathan Jacobson, Rational methods in the theory of Lie algebras, Ann. of Math. (2) 36 (1935), no. 4, 875–881. MR 1503258, DOI 10.2307/1968593

Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), 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.

Shingo Murakami, Sur la classification des algèbres de Lie réelles et simples, Osaka Math. J. 2 (1965), 291–307 (French). MR 201578

I. Satake, Classification theory of semi-simple algebraic groups, Lecture Notes in Pure and Applied Mathematics, vol. 3, Marcel Dekker, Inc., New York, 1971. With an appendix by M. Sugiura; Notes prepared by Doris Schattschneider. MR 0316588

Martin Selbach, Klassifikationstheorie halbeinfacher algebraischer Gruppen, Bonner Mathematische Schriften, Nr. 83, Universität Bonn, Mathematisches Institut, Bonn, 1976. Diplomarbeit, Univ. Bonn, Bonn, 1973. MR 0432776

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

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, pp. 33–62. MR 0224710

1.

B. N. Allison, Isomorphism of simple Lie algebras, Trans. Amer. Math. Soc. 117 (1973), 173-190. MR 48 #6194. MR 0327852

2.

S. Araki, On root systems and an infinitesimal classification of irreducible symmetric spaces, J. Math. Osaka City Univ. 13 (1962), 1-34. MR 27 #3743. MR 153782

3.

A. Borel and J. Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55-150. MR 34 #7527. MR 207712

4.

E. Cartan, Les groupes réels simples, finis et continus, Ann. Sci. École Norm. Sup. (3) 31 (1914), 263-355. MR 1509178

5.

F. Gantmacher, On the classification of real simple Lie groups, Mat. Sb. 5 (1939), 217-249. MR 2, 5. MR 2141

6.

N. Jacobson, Rational methods in the theory of Lie algebras, Ann. of Math. (2) 36 (1935), 875-881. MR 1503258

7.

N. Jacobson, Exceptional Lie algebras, Dekker, New York, 1971. MR 44 #1707. MR 143793

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.

S. Murakami, Sur la classification des algébres de Lie réelles et simples, Osaka J. Math. 2 (1965), 291-307. MR 34 # 1460. MR 201578

11.

I. Satake, Classification theory of semi-simple algebraic groups, Dekker, New York, 1971. MR 47 #5135. MR 316588

12.

M. Selbach, Klassifikationstheorie halbeinfacher algebraischer Gruppen, Bonner Math. Schriften 83 (1976). MR 432776

13.

J. Tits, Une class d'algèbres de Lie en relation avec les algèbres de Jordan, Indag. Math. 24 (1962), 530-535. MR 26 #3753. MR 146231

14.

J. Tits, Classification of algebraic semisimple groups, Proc. Sympos. Pure Math. vol. 9, Amer. Math. Soc., Providence, R. I., 1966, pp. 33-62. MR 37 #309. MR 224710