Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the classification of metabelian Lie algebras


Author: Michael A. Gauger
Journal: Trans. Amer. Math. Soc. 179 (1973), 293-329
MSC: Primary 17B30
DOI: https://doi.org/10.1090/S0002-9947-1973-0325719-0
MathSciNet review: 0325719
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The classification of 2-step nilpotent Lie algebras is attacked by a generator-relation method. The main results are in low dimensions or a small number of relations.


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

  • [1] H. W. Turnbull and A. C. Aitken, An introduction to the theory of canonical matrices, Dover, New York, 1961. MR 23 #A906. MR 0123581 (23:A906)
  • [2] E. Artin, Geometric algebra, Interscience, New York and London, 1957. MR 18, 553. MR 0082463 (18:553e)
  • [3] A Borel, Linear algebraic groups, Benjamin, New York, 1969. MR 40 #4273. MR 0251042 (40:4273)
  • [4] N. Bourbaki, Éléments de mathématique. XXVI. Groupes et algèbres de Lie. Chap. 1: Algèbre de Lie, Actualités Sci. Indust., no. 1285, Hermann, Paris, 1960. MR 24 #A2641.
  • [5] -, Éléments de mathématique. I: Les structures fondamentales de l'analyse. Fasc. VII Livre II: Algèbre. Chap. 3: Algèbre multilinéaire, Actualités Sci. Indust., no. 1044, Hermann, Paris, 1948. MR 10, 231.
  • [6] J. B. Carrell and J. A. Dieudonné, Invariant theory, old and new, Advances in Math 4 (1970), 1-80. MR 41 #186. MR 0255525 (41:186)
  • [7] C. Y. Chao, Uncountably many nonisomorphic nilpotent Lie algebras, Proc. Amer. Math. Soc. 13 (1962), 903-906. MR 26 #6221. MR 0148715 (26:6221)
  • [8] J. Dieudonné, Sur la réduction canonique des couples de matrices, Bull. Soc. Math. France 74 (1946), 130-146. MR 9, 264. MR 0022826 (9:264f)
  • [9] J. Dixmier, Sur les représentations unitaires des groupes de Lie nilpotents. IV, Canad. J. Math. 11 (1959), 321-344. MR 21 #5693. MR 0106963 (21:5693)
  • [10] J. Dixmier and W. G. Lister, Derivations of nilpotent Lie algebras, Proc. Amer. Math. Soc. 8 (1957), 155-158. MR 18, 659. MR 0083101 (18:659a)
  • [11] F. Gantmacher, The theory of matrices, GITTL, Moscow, 1953; English transl., Chelsea, New York, 1959. MR 16, 438; MR 21 # 6372c.
  • [12] M. Gauger, Thesis, Notre Dame, Ind., 1971.
  • [13] G. B. Gurevič, On metabelian Lie algebras, Trudy Sem. Vektor. Tenzor. Anal. 12 (1963), 9-61. (Russian) MR 28 #1217. MR 0157989 (28:1217)
  • [14] W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry. Vols. 1, 2, Cambridge Univ. Press, Cambridge, 1947, 1952. MR 10, 396; MR 13, 972.
  • [15] N. Jacobson, Lie algebras, Interscience Tracts in Pure and Appl. Math., no. 10, Interscience, New York, 1962. MR 26 # 1345. MR 0143793 (26:1345)
  • [16] -, Lectures in abstract algebra. Vol. II. Linear algebra, Van Nostrand, Princeton, N. J., 1953. MR 14, 837. MR 0053905 (14:837e)
  • [17] -, A note on automorphisms and derivations of Lie algebras, Proc. Amer. Math. Soc. 6 (1955), 281-283. MR 16, 897. MR 0068532 (16:897e)
  • [18] C. C. MacDuffee, Theory of matrices, Springer, Berlin, 1933; reprint, Chelsea, New York, 1946.
  • [19] S. Mac Lane and G. Birkhoff, Algebra, Macmillan, New York, 1967. MR 35 #5266. MR 0214415 (35:5266)
  • [20] A. I. Mal'cev, Solvable Lie algebras, Izv. Akad. Nauk SSSR Ser. Mat. 9 (1945), 329-356; English transl., Amer. Math. Soc. Transl. (1) 9 (1962), 228-262. MR 9, 173. MR 0022217 (9:173f)
  • [21] A. I. Mal'cev, On a class of homogeneous spaces, Izv. Akad. Nauk SSSR Ser. Mat. 13 (1949), 9-32; English transl., Amer. Math. Soc. Transl. (1) 9 (1962), 276-307 MR 10, 507. MR 0028842 (10:507d)
  • [22] V. V. Morozov, Classification of nilpotent Lie algebras of sixth order, Izv. Vysš. Učebn. Zaved. Matematika 1958, no. 4 (5), 161-171. (Russian) MR 24 #A190. MR 0130326 (24:A190)
  • [23] D. Mumford, Introduction to algebraic geometry, Harvard Univ. Press, Cambridge, Mass.
  • [24] J. Scheuneman, Two-step nilpotent Lie algebras, J. Algebra 7 (1967), 152-159. MR 36 #225. MR 0217134 (36:225)
  • [25] G. Seligman, Algebraic groups, Lectures Notes, Yale University, New Haven, Conn., 1964.
  • [26] M. Gauger, Duality theories for metabelian Lie algebras, Trans. Amer. Math. Soc. (to appear). MR 0342576 (49:7322)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 17B30

Retrieve articles in all journals with MSC: 17B30


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0325719-0
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society