Operadic quantization of some 3d Lie algebras over harmonic oscillator

  • Eugen Paal, Jüri Virkepu
  • Published 2009

Abstract

Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of some 3d real Lie algebras in Bianchi classification. The Jacobians of these quantum algebras arecalculated. It is conjectured that the tangent algebras of these quantum algebras are the Heisenberg algebra. From this it follows that the volume element in R has discrete values: |(x, y, z)| = 4 √ 2(2n+ 1) (n = 0, 1, 2, . . . ).

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Cite this paper

@inproceedings{Paal2009OperadicQO, title={Operadic quantization of some 3d Lie algebras over harmonic oscillator}, author={Eugen Paal and J{\"{u}ri Virkepu}, year={2009} }