相关论文: Twisted geometry for submanifolds of $\mathbb{R}^n…
We propose a general procedure to construct noncommutative deformations of an embedded submanifold $M$ of $\mathbb{R}^n$ determined by a set of smooth equations $f^a(x)=0$. We use the framework of Drinfel'd twist deformation of differential…
We propose a general procedure to construct noncommutative deformations of an algebraic submanifold $M$ of $\mathbb{R}^n$, specializing the procedure [G. Fiore, T. Weber, Twisted submanifolds of $\mathbb{R}^n$, arXiv:2003.03854] valid for…
We consider noncommutative geometries obtained from a triangular Drinfeld twist. This allows to construct and study a wide class of noncommutative manifolds and their deformed Lie algebras of infinitesimal diffeomorphisms. This way symmetry…
In this thesis we give obstructions for Drinfel'd twist deformation quantization on several classes of symplectic manifolds. Motivated from this quantization procedure, we further construct a noncommutative Cartan calculus on any braided…
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…
We investigate deformed superconformal symmetries on non(anti)commutative (super)spaces from the point of view of the Drinfel'd twisted symmetries. We classify all possible twist elements derived from an abelian subsector of the…
We consider noncommutative geometries obtained from a triangular Drinfeld twist and review the formulation of noncommutative gravity. A detailed study of the abelian twist geometry is presented, including the fundamental theorem of…
In this paper we consider gauge theories that are relativistic and scale-invariant, and we construct their deformed versions via suitable star products. In particular, the non-commutative structure is controlled by Drinfel'd twists that are…
A new non-standard deformation of all types of classical Lie algebras is constructed by means of Drinfel'd twist based on a six dimensional subalgebra. This is an extension of extended twists introduced by Kulish et al. For the algebra M_3…
Covariance ties the noncommutative deformation of a space into a quantum space closely to the deformation of the symmetry into a quantum symmetry. Quantum deformations of enveloping algebras are governed by Drinfeld twists, inner…
We propose Weil and Cartan models for the equivariant cohomology of noncommutative spaces which carry a covariant action of Drinfel'd twisted symmetries. The construction is suggested by the noncommutative Weil algebra of Alekseev and…
We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative…
We present a simple no-go theorem for the existence of a deformation quantization of a homogeneous space M induced by a Drinfel'd twist: we argue that equivariant line bundles on M with non-trivial Chern class and symplectic twist star…
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…
In this paper, we describe nonstandard quantum deformation of the super-Virasoro algebra. Using the Drinfel'd twist quantization technique, we obtain the deformed coproduct and antipode. Hence we get a family of noncommutative and…
These notes refer to a minicourse I gave at the occasion of the conference meeting ``Applications of Noncommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time'' to be held from 7 April to 11 April 2025 at the Centre…
This is the final version of my master thesis. I prove that there are no twist star products on the 2-sphere and on the higher genus pretzel surfaces deforming a symplectic structure. One of the key arguments is that a connected compact…
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…
Universal Drinfeld twists are inner automorphisms which relate the coproduct of a quantum enveloping algebra to the coproduct of the undeformed enveloping algebra. Even though they govern the deformation theory of classical symmetries and…
We discuss the quantum Poincar\'e symmetries of the $\varrho$-Minkowski spacetime, a space characterised by an angular form of noncommutativity. We show that it is possible to give them both a bicrossproduct and a Drinfel'd twist structure.…