Related papers: Hopf Algebras in Deformed Quantum Theories
We study the relationship between antipodes on a Hopf algebroid $\mathcal{H}$ in the sense of B\"ohm-Szlachanyi and the group of twists that lies inside the associated convolution algebra. We specialize to the case of a faithfully flat…
We construct explicit Drinfel'd twists of Jordanian type for the generalized Cartan type K Lie algebras in characteristic 0 and obtain the corresponding quantizations, especially their integral forms. By making modular reductions including…
The subject of this paper are two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the multiplication, while the second group is the…
The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash…
We introduce a noncommutative and noncocommutative Hopf algebra which takes for certain Hopf categories (and therefore braided monoidal bicategories) a similar role as the Grothendieck- Teichmueller group for quasitensor categories. We also…
In this paper, we use the general quantization method by Drinfel'd twists to quantize the Schr\"odinger-Virasoro Lie algebra whose Lie bialgebra structures were recently discovered by Han-Li-Su. We give two different kinds of Drinfel'd…
We show that deformed Heisenberg algebra with reflection emerging in parabosonic constructions is also related to parafermions. This universality is discussed in different algebraic aspects and is employed for the description of spin-j…
We discuss a generalisation of the Snyder model that includes all the possible deformations of the Heisenberg algebra compatible with Lorentz invariance, in terms of realisations of the noncommutative geometry. The corresponding deformed…
The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to…
This paper establishes several fundamental structural properties of the $q$-Heisenberg algebra $\mathfrak{h}_n(q)$, a quantum deformation of the classical Heisenberg algebra. We first prove that when $q$ is not a root of unity, the global…
We parameterize the finite-dimensional irreducible representations of a class of pointed Hopf algebras over an algebraically closed field of characteristic zero by dominant characters. The Hopf algebras we are considering arise in the work…
The non-singular bouncing solution of loop quantum cosmology is reproduced by a deformed minisuperspace Heisenberg algebra. This algebra is a realization of the Snyder space, is almost unique and is related to the $\kappa$-Poincar\'e one.…
We establish the existence of a quasi-Hopf algebraic structure underlying the Leigh-Strassler N=1 superconformal marginal deformations of the N=4 Super-Yang-Mills theory. The scalar-sector R-matrix of these theories, which is related to…
Universal $T$-matrices, or Hopf algebra dual forms, for quantum groups are revisited, and their contraction theory is developed. As a first illustrative example, the (1+1) timelike $\kappa$-Poincar\'e $T$-matrix is explicitly worked out.…
We contruct here the Hopf algebra structure underlying the process of renormalization of non-commutative quantum field theory.
We describe three ways of modifying the relativistic Heisenberg algebra - first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of…
We report the results obtained in the study of Alain Connes noncommutative spectral geometry construction focusing on its essential ingredient of the algebra doubling. We show that such a two-sheeted structure is related with the gauge…
Starting from a faithful five-dimensional matrix representation of the group of two independent oscillators and applying the R-matrix method we generate some classes of deformed fermionic-bosonic quantum Hopf algebras. The corresponding Lie…
The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted co-product. This allows for the definition of conformal symmetry in a non-commutative background geometry. The twisted co-product is reviewed for the…
In a previous paper, we investigated the Hopf algebra structure in string theory and gave a unified formulation of the quantization of the string and the space-time symmetry. In this paper, this formulation is applied to the case with a…