Journal of Generalized Lie Theory and Applications

Operadic representations of harmonic oscillator in some 3d algebras

Eugen PAAL and Juri VIRKEPU

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It is explained how the time evolution of the operadic variables may be introduced by using the operadic Lax equation. The operadic Lax representations for the harmonic oscillator are constructed in 3-dimensional binary anti-commutative algebras. As an example, an operadic Lax representation for the harmonic oscillator in the Lie algebra $\mathfrak{sl}(2)$ is constructed.

Article information

J. Gen. Lie Theory Appl., Volume 3, Number 1 (2009), Article ID S090104, 53-60.

First available in Project Euclid: 19 October 2011

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Zentralblatt MATH identifier

Primary: 18D50: Operads [See also 55P48] 70G60: Dynamical systems methods


PAAL, Eugen; VIRKEPU, Juri. Operadic representations of harmonic oscillator in some 3d algebras. J. Gen. Lie Theory Appl. 3 (2009), no. 1, Article ID S090104, 53--60. doi:10.4303/jglta/S090104.

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