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)

 
 

 

A note on Lie-admissible nilalgebras


Author: Hyo Chul Myung
Journal: Proc. Amer. Math. Soc. 31 (1972), 95-96
DOI: https://doi.org/10.1090/S0002-9939-1972-0291230-3
MathSciNet review: 0291230
Full-text PDF

Abstract | References | Additional Information

Abstract: It is shown that a finite dimensional, flexible, powerassociative, Lie-admissible algebra $ \mathfrak{A}$ over a field of characteristic 0 is a nilalgebra if and only if there exists a Cartan subalgebra of $ {\mathfrak{A}^ - }$- which is nil in $ \mathfrak{A}$.


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

  • [1] C. Chevalley, Théorie des groupes de Lie, Hermann, Paris, 1968.
  • [2] P. J. Laufer and M. L. Tomber, Some Lie admissible algebras, Canad. J. Math. 14 (1962), 287-292. MR 25 #104. MR 0136636 (25:104)
  • [3] H. C. Myung, A remark on the proof of a theorem of Laufer and Tomber, Canad. J. Math. 23 (1971), 270. MR 0269707 (42:4602)
  • [4] R. H. Oehmke, On flexible algebras, Ann. of Math. (2) 68 (1958), 221-230. MR 21 #5664. MR 0106934 (21:5664)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0291230-3
Keywords: Flexible algebra, Lie-admissible algebra, Cartan subalgebra
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society