Related papers: A Counter Example of Invariant Deformation Quantiz…

We apply the star product quantization to the Lie algebra. The quantization in terms of the star product is well known and the commutation relation in this case is called the $\theta$-deformation where the constant $\theta$ appears as a…

We present a star product for noncommutative spaces of Lie type, including the so called ``canonical'' case by introducing a central generator, which is compatible with translations and admits a simple, manageable definition of an invariant…

Using duality and topological theory of well behaved Hopf algebras (as defined in [2]) we construct star-product models of non compact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple…

We study the general form of the noncommutative associative product (the star-product) on the Grassman algebra; the star-product is treated as a deformation of the usual "pointwise" product. We show that up to a similarity transformation,…

We develop a complete theory of non-formal deformation quantization on the cotangent bundle of a weakly exponential Lie group. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…

I have chosen, in this presentation of Deformation Quantization, to focus on 3 points: the uniqueness --up to equivalence-- of a universal star product (universal in the sense of Kontsevich) on the dual of a Lie algebra, the cohomology…

This set of notes corresponds to a mini-course given in September 2018 in Bedlewo; it does not contain any new result; it complements -- with intersection -- the introduction to formal deformation quantization and group actions,…

We study deformation quantization on an infinite-dimensional Hilbert space $W$ endowed with its canonical Poisson structure. The standard example of the Moyal star-product is made explicit and it is shown that it is well defined on a…

Let G be a connected reductive group over an algebraically closed field K of characteristic 0, X an affine symplectic variety equipped with a Hamiltonian action of G. Further, let * be a G-invariant Fedosov star-product on X such that the…

We consider the noncommutative space-times with Lie-algebraic noncommutativity (e.g. $\kappa$-deformed Minkowski space). In the framework with classical fields we extend the $\star$-product in order to represent the noncommutative…

The use of a diffeomorphism covariant star product enables us to construct diffeomorphism invariant gravities on noncommutative symplectic manifolds without twisting the symmetries. As an example, we construct noncommutative deformations of…

We associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. In the limit of a contraction to a Schr\"odinger algebra, these equations…

Two main problems face the construction of noncommutative actions for gravity with star products: the complex metric and finding an invariant measure. The only gauge groups that could be used with star products are the unitary groups. I…

A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…

Let $\mathbb B$ be a Lie group admitting a left-invariant negatively curved K\"ahlerian structure. Consider a strongly continuous action $\alpha$ of $\mathbb B$ on a Fr\'echet algebra $\mathcal A$. Denote by $\mathcal A^\infty$ the…

We classify Lie n-algebras possessing an invariant lorentzian inner product.

Two examples of $\mathrm{Diff}^+S^1$-invariant closed two-forms obtained from forms on jet bundles, which does not admit equivariant moment maps are presented. The corresponding cohomological obstruction is computed and shown to coincide…

We give an invariant formula for a star product with separation of variables on a pseudo-Kahler manifold.

We consider linear star products on $R^d$ of Lie algebra type. First we derive the closed formula for the polydifferential representation of the corresponding Lie algebra generators. Using this representation we define the Weyl star product…

Using techniques of deformation (bi)quantization we establish a non-canonical algebra isomorphism between the deformed reduction algebra and the invariant differential operators on G/H. Further results concerning other deformations of these…