Related papers: The Pegg-Barnett oscillator and its supersymmetric…
An attempt had been made to get algebraic structure of 2D complex harmonic oscillator.
A static minimal energy configuration of a super p-brane in a supersymmetric (n+1)-dimensional spacetime is shown to be a `generalized calibrated' submanifold. Calibrations in $\bE^{(1,n)}$ and $AdS_{n+1}$ are special cases. We present…
We study the Lie algebra structure of the Onsager algebra from the ideal theoretic point of view. A structure theorem of ideals in the Onsager algebra is obtained with the connection to the finite-dimensional representations. We also…
In our paper Semi-symmetric Algebras: General Constructions, J. Algebra, 148 (1992), pp. 479-496, we present the construction of the semi-symmetric algebra of a module over a commutative ring with unit, which generalizes the tensor algebra,…
Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide applications in modern physics and connection to many domains in…
In these lectures we study some possible higher order (of degree greater than two) extensions of the Poincar\'e algebra. We first give some general properties of Lie superalgebras with some emphasis on the supersymmetric extension of the…
We construct and discuss the Fock-space representation for a deformed oscillator with "peculiar" statistics. We show that corresponding algebra represents deformed supersymmetric oscillator.
We present a detailed study of a parametric Lie algebra encompassing the symmetry algebras of various models, both continuous and discrete. This algebraic structure characterizes the isotropic oscillator (with positive, purely imaginary,…
All possible Lie bialgebra structures on the harmonic oscillator algebra are explicitly derived and it is shown that all of them are of the coboundary type. A non-standard quantum oscillator is introduced as a quantization of a triangular…
Oscillator Lie algebras are the only non commutative solvable Lie algebras which carry a bi-invariant Lorentzian metric. In this paper, we determine all the Poisson structures, and in particular, all symmetric Leibniz algebra structures…
The purpose of this study is to extend the concept of a generalized Lie $3-$ algebra, known to the divisional algebra of the octonions $\mathbb{O}$, to split-octonions $\mathbb{SO}$, which is non-divisional. This is achieved through the…
In this paper, Lie superbialgebra structures on the centerless twisted N=2 superconformal algebra $\LL$ are considered which are proved to be coboundary triangular.
A study is made of real Lie algebras admitting a hypersymplectic structure, and we provide a method to construct such hypersymplectic Lie algebras. We use this method in order to obtain the classification of all hypersymplectic structures…
Parabosonic $P_{B}^{(n)}$ and parafermionic $P_{F}^{(n)}$ algebras are described as quotients of the tensor algebras of suitably choosen vector spaces. Their (super-) Lie algebraic structure and consequently their (super-) Hopf structure is…
We consider an N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator with distinct frequencies of oscillation. The technique previously developed in [Acta Phys. Polon. B 36 (2005) 2115; Nucl. Phys. B 902 (2016) 95] is used to construct a…
The extension of the noncommutative u*(N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u*(N) can consistently be restricted to o*(N)…
The spectral and localization properties of $\mathcal{PT}$-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are…
In this work we investigate connections between superalgebras and their realizations in terms of particles, branes and field theory models. We start from Poincar\'e superalgebras with brane charges and study its representations. The…
We study the spectrum generating closed nonlinear superconformal algebra that describes $\mathcal{N}=2$ super-extensions of rationally deformed quantum harmonic oscillator and conformal mechanics models with coupling constant $g=m(m+1)$,…
Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional…