Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Constructing bases for radicals and nilradicals of Lie algebras


Author: Stephen Merrin
Journal: Proc. Amer. Math. Soc. 119 (1993), 681-690
MSC: Primary 17B05; Secondary 03F65
MathSciNet review: 1152285
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The radical and nilradical of a finite-dimensional Lie algebra $ L$ are well defined unique subspaces of $ L$. Nevertheless, we show the impossibility of ever finding a general algorithm that will construct finite bases for radicals (or nilradicals) of arbitrary finite-dimensional Lie algebras. Our approach involves an investigation of the relationship between radicals of associative algebras and radicals of Lie algebras. Building on a result of Richman in the constructive theory of associative algebras, we prove that bases for radicals and nilradicals of finite-dimensional Lie algebras over a discrete field $ F$ can always be constructed if and only if $ F$ satisfies Seidenberg's condition P. A special case is that if we restrict ourselves to fields of characteristic zero, we can indeed always construct bases for radicals. Our proofs are entirely constructive (i.e., do not use the general law of excluded middle).


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17B05, 03F65

Retrieve articles in all journals with MSC: 17B05, 03F65


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1152285-0
PII: S 0002-9939(1993)1152285-0
Keywords: Lie algebra, constructive algebra, radical, nilradical
Article copyright: © Copyright 1993 American Mathematical Society