相关论文: Real Forms of the Oscillator Quantum Algebra and i…
We consider three quantum algebras: the q-oscillator algebra, the Podles' sphere and the q-deformed enveloping algebra of $su(2).$ To each of these *-algebras we associate certain partial dynamical system and perform the "Mackey analysis"…
Nonlinear $sl(2)$ algebras subtending generalized angular momentum theories are studied in terms of undeformed generators and bases. We construct their unitary irreducible representations in such a general context. The linear $sl(2)$-case…
Multiparametric quantum $gl(2)$ algebras are presented according to a classification based on their corresponding Lie bialgebra structures. From them, the non-relativistic limit leading to quantum harmonic oscillator algebras is implemented…
We show that the quantum Heisenberg group $H_{q}(1)$ can be obtained by means of contraction from quantum $SU_q(2)$ group. Its dual Hopf algebra is the quantum Heisenberg algebra $U_{q}(h(1))$. We derive left and right regular…
We associate to any (suitable) bicovariant differential calculus on a quantum group a Cartan Hopf algebra which has a left, respectively right, representation in terms of left, respectively right, Cartan calculus operators. The example of…
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from \fun\ to \uqg\ , given by elements of the pure braid group. These operators --- the `reflection matrix' $Y \equiv…
We define for real $q$ a unital $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ quantizing the universal enveloping $*$-algebra of $\mathfrak{sl}(2,\mathbb{R})$. The $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ is realized as a…
These notes present a quick introduction to the q-deformations of semisimple Lie groups from the point of view of unitary representation theory. In order to remain concrete, we concentrate entirely on the case of the lie algebra…
The properties of the quantum Minkowski space algebra are discussed. Its irreducible representations with highest weight vectors are constructed and relations to other quantum algebras: $su_{q}(2)$, $q$-oscillator, $q$-sphere are pointed…
Two coalgebra structures are used in quantum field theory. The first one is the coalgebra part of a Hopf algebra leading to deformation quantization. The second one is a co-module co-algebra over the first Hopf algebra and it is used to…
We introduce a category of $q$-oscillator representations over the quantum affine superalgebras of type $D$ and construct a new family of its irreducible representations. Motivated by the theory of super duality, we show that these…
The $q$--deformation $U_q (h_4)$ of the harmonic oscillator algebra is defined and proved to be a Ribbon Hopf algebra.Associated with this Hopf algebra we define an infinite dimensional braid group representation on the Hilbert space of the…
The quantum superalgebra $U_q[gl(2/1)]$ is given as both a Drinfel'd--Jimbo deformation of $U[gl(2/1)]$ and a Hopf superalgebra. Finite--dimensional representations of this quantum superalgebra are constructed and investigated in a basis of…
The quantum double construction of a $q$-deformed boson algebra possessing a Hopf algebra structure is carried out explicitly. The $R$-matrix thus obtained is compared with the existing literature.
Certain types of generalized undeformed and deformed boson algebras which admit a Hopf algebra structure are introduced, together with their Fock-type representations and their corresponding $R$-matrices. It is also shown that a class of…
The operator algebras of a new family of relativistic geometric models of the relativistic oscillator are studied. It is shown that, generally, the operator of number of quanta and the pair of the shift operators of each model are the…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
By starting from the non-standard quantum deformation of the sl(2,R) algebra, a new quantum deformation for the real Lie algebra so(2,2) is constructed by imposing the former to be a Hopf subalgebra of the latter. The quantum so(2,2)…
Hopf representation is a module and comodule with a consistency condition that is more general than the consistency condition of Hopf modules. For a Hopf algebra $H$, we construct an induced Hopf representation from a representation of a…
The various relations between $q$-deformed oscillators algebras and the $q$-deformed $su(2)$ algebras are discussed. In particular, we exhibit the similarity of the $q$-deformed $su(2)$ algebra obtained from $q$-oscillators via Schwinger…