J. Van der Jeugt

collaborators

4 papers

math-ph2025

A class of representations of the $Z_{2} \times Z_{2}$ -graded special linear Lie superalgebra $sl (m_{1} + 1, m_{2} ∣ n_{1}, n_{2})$ and quantum statistics

N. I. Stoilova, J. Van der Jeugt

The description of the $Z_{2} \times Z_{2}$ -graded special linear Lie superalgebra $sl (m_{1} + 1, m_{2} ∣ n_{1}, n_{2})$ is carried out via generators $a_1^\pm,\ldots, a_…

math-ph2025

$Z_{2}^{3}$ -grading of the Lie algebra $G_{2}$ and related color algebras

N. I. Stoilova, J. Van der Jeugt

We present a special and attractive basis for the exceptional Lie algebra $G_{2}$ , which turns $G_{2}$ into a $Z_{2}^{3}$ -graded Lie algebra. There are two basis elements for each…

quant-ph2025

Deformation of the Heisenberg-Weyl algebra and the Lie superalgebra $osp (1∣2)$ : exact solution for the quantum harmonic oscillator with a position-dependent mass

E. I. Jafarov, S. M. Nagiyev, J. Van der Jeugt

We propose a new deformation of the quantum harmonic oscillator Heisenberg-Weyl algebra with a parameter $a > - 1$ . This parameter is introduced through the replacement of the homogen…

math-ph2024

Generalized boson and fermion operators with a maximal total occupation property

N. I. Stoilova, J. Van der Jeugt

We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symm…

A class of representations of the Z2​×Z2​-graded special linear Lie superalgebra sl(m1​+1,m2​∣n1​,n2​) and quantum statistics

Z23​-grading of the Lie algebra G2​ and related color algebras

Deformation of the Heisenberg-Weyl algebra and the Lie superalgebra osp(1∣2): exact solution for the quantum harmonic oscillator with a position-dependent mass

Generalized boson and fermion operators with a maximal total occupation property

A class of representations of the $Z_{2} \times Z_{2}$ -graded special linear Lie superalgebra $sl (m_{1} + 1, m_{2} ∣ n_{1}, n_{2})$ and quantum statistics

$Z_{2}^{3}$ -grading of the Lie algebra $G_{2}$ and related color algebras

Deformation of the Heisenberg-Weyl algebra and the Lie superalgebra $osp (1∣2)$ : exact solution for the quantum harmonic oscillator with a position-dependent mass