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Jyri Virkepu

Publications and source records attributed to Jyri Virkepu.

7 recordsLinked to original sources
arXiv2009

Dynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator

Operadic Lax representations for the harmonic oscillator are used to construct the dynamical deformations of three-dimensional (3D) real Lie algebras in the Bianchi classification. It is shown that the energy conservation of the harmonic oscillator is related to the Jacobi identities of the dynamically deformed algebras. Based on this observation, it is proved that the dynamical deformations of 3D real Lie algebras in the Bianchi classification over the harmonic oscillator are Lie algebras.

math.RT↗
arXiv2009

3D binary anti-commutative operadic Lax representations for harmonic oscillator

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 sl(2) is constructed.

math-ph↗
arXiv2008

Note on 2d binary operadic harmonic oscillator

It is explained how the time evolution of the operadic variables may be introduced. As an example, a 2-dimensional binary operadic Lax representation of the harmonic oscillator is found.

math-ph↗
arXiv2008

Note on operadic harmonic oscillator

It is explained how the time evolution of the operadic variables may be introduced. As an example, an operadic Lax representation of the harmonic oscillator is considered.

math-ph↗
arXiv2007

How to compose Lagrangian?

A method for constructing Lagrangians for the Lie transformation groups is explained. As examples, the Lagrangians for real plane rotations and affine transformations of the real line are constructed.

math-ph↗
arXiv2005

Plane rotations and Hamilton-Dirac mechanics

Canonical formalism for SO(2) is developed. This group can be seen as a toy model of the Hamilton-Dirac mechanics with constraints. The Lagrangian and Hamiltonian are explicitly constructed and their physical interpretation are given. The Euler-Lagrange and Hamiltonian canonical equations coincide with the Lie equations. It is shown that the constraints satisfy CCR. Consistency of the constraints is checked.

math-ph↗