Constructing bases for radicals and nilradicals of Lie algebras
Author:
Stephen Merrin
Journal:
Proc. Amer. Math. Soc. 119 (1993), 681690
MSC:
Primary 17B05; Secondary 03F65
MathSciNet review:
1152285
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Abstract: The radical and nilradical of a finitedimensional Lie algebra are well defined unique subspaces of . Nevertheless, we show the impossibility of ever finding a general algorithm that will construct finite bases for radicals (or nilradicals) of arbitrary finitedimensional 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 finitedimensional Lie algebras over a discrete field can always be constructed if and only if 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).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311522850
PII:
S 00029939(1993)11522850
Keywords:
Lie algebra,
constructive algebra,
radical,
nilradical
Article copyright:
© Copyright 1993
American Mathematical Society
