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2010 Canonical endomorphism field on a Lie algebra
J. Gen. Lie Theory Appl. 4: 1-17 (2010). DOI: 10.4303/jglta/G100302


We show that every Lie algebra is equipped with a natural (1,1)-variant tensor field, the "canonical endomorphism field", determined by the Lie structure, and satisfying a certain Nijenhuis bracket condition. This observation may be considered as complementary to the Kirillov-Kostant-Souriau theorem on symplectic geometry of coadjoint orbits. We show its relevance for classical mechanics, in particular for Lax equations. We show that the space of Lax vector fields is closed under Lie bracket and we introduce a new bracket for vector fields on a Lie algebra. This bracket defines a new Lie structure on the space of vector fields.


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Jerzy KOCIK. "Canonical endomorphism field on a Lie algebra." J. Gen. Lie Theory Appl. 4 1 - 17, 2010.


Published: 2010
First available in Project Euclid: 11 October 2011

zbMATH: 1298.70022
MathSciNet: MR2795573
Digital Object Identifier: 10.4303/jglta/G100302

Primary: 17B08 , 53C15 , 53C80 , 70G45 , 70G60 , 70H03 , 70H05

Rights: Copyright © 2010 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

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