Related papers: Cartan Pairs
A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed in q-alg/9609011 In this paper we give an outline of the construction of a noncommutative analogy of the algebra of partial…
In this paper, we revise the concept of noncommutative vector fields introduced previously in Ref. [1,2], extending the framework, adding new results and clarifying the old ones. Using appropriate algebraic tools certain shortcomings in the…
For a more general notion of Cartan connection we define characteristic classes, we investigate their relation to usual characteristic classes.
We give in this paper which is the fifth in a series of eight a theory of covariant derivatives of multivector and extensor fields based on the geometric calculus of an arbitrary smooth manifold M, and the notion of a connection extensor…
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector…
The purpose of this paper is to put into a noncommutative context basic notions related to vector fields from classical differential geometry. The manner of exposition is an attempt to make the material as accessible as possible to…
The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of…
Cartan calculi on the extended quantum superplane are given. To this end, the noncommutative differential calculus on the extended quantum superplane is extended by introducing inner derivations and Lie derivatives.
The aim of this article is to characterize pairs of curves within multiplicative (non-Newtonian) spaces. Specifically, we investigate how famous curve pairs such as Bertrand partner curves, Mannheim partner curves, which are prominent in…
To give a Cartan calculus on the extended quantum 3d space, the noncommutative differential calculus on the extended quantum 3d space is extended by introducing inner derivations and Lie derivatives.
A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum groups, we…
A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine…
We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…
The aim of this paper is to avoid some difficulties, related with the Lie bracket, in the definition of vector fields in a non commutative setting, as they were defined by Woronowicz, Schmudgen--Schuler and Aschieri--Schupp. We extend the…
We define what we call morphisms of Cartan connections. We generalize the main theorems on Cartan connections to theorems on morphisms. Many of the known constructions involving Cartan connections turn out to be examples of morphisms. We…
We give a differential geometric description of the Cartan (or tractor) bundle and its canonical connection in CR geometry, thus offering a direct, alternative, definition to the usual abstract approach.
We examine the N-Koszul calculus for the N-symmetric algebras. The case N=2 corresponds to the Elie Cartan calculus. We conjecture that, as in the case N=2, the N-Cartan calculus extends to manifolds when N>2, which would provide a new type…
We extend the universal differential calculus on an arbitrary Hopf algebra to a ``universal Cartan calculus''. This is accomplished by introducing inner derivations and Lie derivatives which act on the elements of the universal differential…
In this paper we will provide a new operatorial counterpart of the path-integral formalism of classical mechanics developed in recent years. We call it new because the Jacobi fields and forms will be realized via finite dimensional…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…