Related papers: Topological Quantum Groups, Star Products and thei…
For compact quantizable K\"ahler manifolds certain naturally defined star products and their constructions are reviewed. The presentation centers around the Berezin-Toeplitz quantization scheme which is explained. As star products the…
C*-quantum groups with projection are the noncommutative analogues of semidirect products of groups. Radford's Theorem about Hopf algebras with projection suggests that any C*quantum group with projection decomposes uniquely into an…
We study the action of space-time symmetries on quantum fields in the presence of small departures from locality determined by dynamical gravity. It is shown that, under such relaxation of locality, the symmetries of the theory cannot be…
The properties of dense hadronic and quark matter and its relation to compact stars are discussed. In a bottom-up approach one starts with nuclear and hypernuclear physics at low density and extrapolates hadronic matter to large densities.…
Family of doublings of Hopf algeras based on the product of algebra and its dual are constructed and studied. Special cases of these construction may be considered as natural quantum analogs of rings of differential operators on groups.…
Deforming the algebraic structure of geometric algebra on the phase space with a Moyal product leads naturally to supersymmetric quantum mechanics in the star product formalism.
We introduce and study a number of invariants of locally compact quantum groups defined by their scaling and modular groups and the spectrum of their modular elements. Focusing mainly on compact quantum groups we consider the question…
In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and…
We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which based on Weyl symmetrically ordered operator products. By using a polydifferential representation for deformed coordinates…
Hopf crossed products, or in other words, cleft comodule algebras form a special but important class in Hopf-Galois extensions. To discuss this interesting subject, we will start with the more familiar group crossed products, and then see…
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…
In this talk work done by our group on cosmic topology is reviewed. It ranges from early attempts to solve a famous controversy about quasars through the multiplicity of images, to quantum cosmology in this context and an application to QED…
We apply methods from strict quantization of solvable symmetric spaces to obtain universal deformation formulae for actions of a class of solvable Lie groups. We also study compatible co-products by generalizing the notion of smash product…
We re-examine all the contractions related with the ${\cal U}_q(su(2))$ deformed algebra and study the consequences that the contraction process has for their structure. We also show using ${\cal U}_q(su(2))\times{\cal U}(u(1))$ as an…
We show for bicommutative graded connected Hopf algebras that a certain distributive (Laplace) subgroup of the convolution monoid of 2-cochains parameterizes certain well behaved Hopf algebra deformations. Using the Laplace group, or its…
In this paper we study a family of algebraic deformations of regular coadjoint orbits of compact semisimple Lie groups with the Kirillov Poisson bracket. The deformations are restrictions of deformations on the dual of the Lie algebra. We…
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
Given an extension $0\to V\to G\to Q\to1$ of locally compact groups, with $V$ abelian, and a compatible essentially bijective $1$-cocycle $\eta\colon Q\to\hat V$, we define a dual unitary $2$-cocycle on $G$ and show that the associated…
We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$.…
Quantum affine bundles are quantum principal bundles with affine quantum structure groups. A general theory of quantum affine bundles is presented. In particular, a detailed analysis of differential calculi over these bundles is performed,…