Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The first Whitehead lemma for Malcev algebras


Author: Renate Carlsson
Journal: Proc. Amer. Math. Soc. 58 (1976), 79-84
MSC: Primary 17E05
DOI: https://doi.org/10.1090/S0002-9939-1976-0409585-9
MathSciNet review: 0409585
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the present paper the first Whitehead lemma for separable Malcev algebras is proved, the dimensions being finite and the characteristic of the base field necessarily equal to zero. A consequence is the theorem of Malcev-Harish-Chandra for Malcev algebras. To get the lemma a structure theorem for modules over semisimple split Malcev algebras is proved.


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

  • [1] R. Carlsson, Malcev-Moduln, J. Reine Angew. Math. (to appear). MR 0393158 (52:13968)
  • [2] N. Jacobson, Lie algebras, Interscience Tracts in Pure and Appl. Math., no. 10, Interscience, New York and London, 1962. MR 26 #1345. MR 0143793 (26:1345)
  • [3] E. N. Kuz'min, Mal'cev algebras and their representations, Algebra i Logika 7 (1968), no. 4, 48-69 = Algebra and Logic 7 (1968), 233-244. MR 40 #5688. MR 0252468 (40:5688)
  • [4] -, The locally nilpotent radical of Mal'cev algebras satisfying the $ n$th Engel condition, Dokl. Akad. Nauk SSSR 177 (1967), 508-510 = Soviet Math. Dokl. 8 (1967), 1434-1436. MR 36 #2660. MR 0219581 (36:2660)
  • [5] A. A. Sagle, Malcev algebras, Trans. Amer. Math. Soc. 101 (1961), 426-458. MR 26 #1343. MR 0143791 (26:1343)
  • [6] E. J. Taft, The Whitehead first lemma for alternative algebras, Proc. Amer. Math. Soc. 8 (1957), 950-956. MR 19, 728. MR 0089842 (19:728a)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17E05

Retrieve articles in all journals with MSC: 17E05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0409585-9
Keywords: Malcev algebras, Malcev modules, derivations, Whitehead's first lemma, theorem of Malcev-Harish-Chandra, Lie algebras
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society