11 citations · 42 across the 10 of their papers we have counts for
10 papers
The parity operator for parafermions and parabosons
N. I. Stoilova, J. Van der Jeugt
In this paper we reexamine the definition of parafermions and parabosons by means of Green's triple relations, and extend these relations by including a parity operator which i…
-grading of the Lie algebra and related color algebras
N. I. Stoilova, J. Van der Jeugt
We present a special and attractive basis for the exceptional Lie algebra , which turns into a -graded Lie algebra. There are two basis elements for each…
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…
Orthosymplectic -graded Lie superalgebras and parastatistics
N. I. Stoilova, J. Van der Jeugt
A -graded Lie superalgebra is a -graded algebra with a bracket that satisfies certain graded versions of the symmetry and Jacobi identity.…
On classical -graded Lie algebras
N. I. Stoilova, J. Van der Jeugt
We construct classes of -graded Lie algebras corresponding to the classical Lie algebras, in terms of their defining matrices. For the -graded Lie a…
The exceptional Lie algebra generated by three generators subject to quadruple relations
N. I. Stoilova, J. Van der Jeugt
In this short communication we show how the Lie algebra can easily be described as a free Lie algebra on 3 generators, subject to some simple quadruple relations f…
A Klein operator for paraparticles
N. I. Stoilova, J. Van der Jeugt
It has been known for a long time that there are two non-trivial possibilities for the relative commutation relations between a set of parafermions and a set of parabosons.…
The -graded Lie superalgebras and , and parastatistics Fock spaces
N. I. Stoilova, J. Van der Jeugt
The parastatistics Fock spaces of order corresponding to an infinite number of parafermions and parabosons with relative paraboson relations are constructed. The Fock spaces ar…
On a pair of difference equations for the type orthogonal polynomials and related exactly-solvable quantum systems
E. I. Jafarov, N. I. Stoilova, J. Van der Jeugt
We introduce a pair of novel difference equations, whose solutions are expressed in terms of Racah or Wilson polynomials depending on the nature of the finite-difference step. A nu…
Deformed su(1,1) Algebra as a Model for Quantum Oscillators
Elchin I. Jafarov, Neli I. Stoilova, Joris Van der Jeugt
The Lie algebra can be deformed by a reflection operator, in such a way that the positive discrete series representations of can be extend…