相关论文: Some Remarks on the Representation of the Generali…
A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally,…
We construct and discuss the Fock-space representation for a deformed oscillator with "peculiar" statistics. We show that corresponding algebra represents deformed supersymmetric oscillator.
The representations of the oscillator algebra introduced by Brzezinski et al. (Phys. Lett. B 311 (1993), 202) are classified.
A unified method of calculating structure functions from commutation relations of deformed single-mode oscillator algebras is presented. A natural approach to building coherent states associated to deformed algebras is then deduced.
The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: $GL_q(2)$, $sl_q(2)$, $q$-oscillator algebra ${\cal A}(q)$, and reflection equation algebra.…
The generalized deformed oscillator schemes introduced as unified frameworks of various deformed oscillators are proved to be equivalent, their unified representation leading to a correspondence between the deformed oscillator and the N=2…
We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
We consider a version of generalised $q$-oscillators and some of their applications. The generalisation includes also "quons" of infinite statistics and deformed oscillators of parastatistics. The statistical distributions for different…
The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…
In this paper I consider the polymorpism of representations of universal algebra and tensor product of representations of universal algebra.
A class of well-behaved *-representations of a q-deformed Heisenberg algebra is studied and classified.
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
A star-product formalism describing deformations of the standard quantum mechanical harmonic oscillator is introduced. A number of existing generalized oscillators occur as particular choises of star-products between the elements of the…
The representation theory of the generalized deformed oscillator algebras (GDOA's) is developed. GDOA's are generated by the four operators ${1,a,a^{\dag},N}$. Their commutators and Hermiticity properties are those of the boson oscillator…
In this paper, we propose a full characterization of a generalized $q-$deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the…
Several physical systems (two identical particles in two dimensions, isotropic oscillator and Kepler system in a 2-dim curved space) and mathematical structures (quadratic algebra QH(3), finite W algebra $\bar {\rm W}_0$) are shown to…
An algebraic deformation theory of coalgebra morphisms is constructed.
A universality of deformed Heisenberg algebra involving the reflection operator is revealed. It is shown that in addition to the well-known infinite-dimensional representations related to parabosons, the algebra has also finite-dimensional…
We study formal deformations of multiplication in an operad. This closely resembles Gerstenhaber's deformation theory for associative algebras. However, this applies to various algebras of Loday-type and their twisted analogs. We explicitly…