Operadic representations of harmonic oscillator in some 3d algebras. (English) Zbl 1163.18301

Summary: 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.


18D50 Operads (MSC2010)
70G60 Dynamical systems methods for problems in mechanics
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