Related papers: Quantum co-adjoint orbits of $\MD_4$-groups
In this paper we construct the set of quantum mechanical observables in the Fedosov *-formalism (a coordinate invariant way to do quantum mechanics on any manifold M) of a single free particle that lives on a constant curvature manifold…
Deformation quantization and geometric quantization on K\"ahler manifolds give the mathematical description of the algebra of quantum observables and the Hilbert spaces respectively, where the later forms a representation of quantum…
We find multipullback quantum odd-dimensional spheres equipped with natural $U(1)$-actions that yield the multipullback quantum complex projective spaces constructed from Toeplitz cubes as noncommutative quotients. We prove that the…
A version of quantum orbit method is presented for real forms of equal rank of quantum complex simple groups. A quantum moment map is constructed, based on the canonical isomorphism between a quantum Heisenberg algebra and an algebra of…
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 paper we consider the problem of deformation quantization of the algebra of polynomial functions on coadjoint orbits of semisimple lie groups. The deformation of an orbit is realized by taking the quotient of the universal…
First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us to…
In this paper we make a review of the results obtained in previous works by the authors on deformation quantization of coadjoint orbits of semisimple Lie groups. We motivate the problem with a new point of view of the well known Moyal-Weyl…
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 we construct a deformation quantization of the algebra of polynomials of an arbitrary (regular and non regular) coadjoint orbit of a compact semisimple Lie group. The deformed algebra is given as a quotient of the enveloping…
Spaces of constant curvature and their motion groups are described most naturally in Cartesian basis. All these motion groups also known as CK groups are obtained from orthogonal group by contractions and analytical continuations. On the…
In this paper we describe a multiparameter deformation of the function algebra of a semisimple coadjoint orbit. In the first section we use the representation of the Lie algebra on a generalized Verma module to quantize the Kirillov bracket…
Using the multi-parametric deformation of the algebra of functions on $ \GL{n+1} $ and the universal enveloping algebra $ \U{\igl{n+1}} $, we construct the multi-parametric quantum groups $ \IGLq{n} $ and $ \Uq{\igl{n}} $.
We study two classes of quantum spheres and hyperboloids which are $*$-quantum spaces for the quantum orthogonal group $\mathcal{O}(SO_q(3))$. We construct line bundles over the quantum homogeneous space of invariant elements for the…
Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold ("phase space"). His algorithm gives a non-commutative, but…
4-manifolds have special topological properties which can be used to get a different view on quantum mechanics. One important property (connected with exotic smoothness) is the natural appearance of 3-manifold wild embeddings (Alexanders…
We review recent works concerning deformation quantization of abelian supergroups. Indeed, we expose the construction of an induced representation of the Heisenberg supergroup and an associated pseudodifferential calculus by using…
The coadjoint orbits for the series $B_l,\ C_l$ and $D_l$ are considered in the case when the base point is a multiple of a fundamental weight. A quantization of the big cell is suggested by means of introducing a $\ast$-algebra generated…
In this paper we construct the commutators of the Fedosov * (a generalization of the Moyal star product) on the phase space of S2. It is shown that this product obeys the standard angular momentum commutation relations in ordinary…
In this paper we construct quantum analogs of strata of coadjoint orbits and describe their representations. This kind objects play an important role in describing quantum groups as repeated extensions of quantum strata.