Related papers: Invariant noncommutative connections
We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for…
The main goal of this article is to construct some geometric invariants for the topology of the set $\mathcal{F}$ of flat connections on a principal $G$-bundle $P\,\longrightarrow\, M$. Although the characteristic classes of principal…
We introduce a class of $G$-invariant connections on a homogeneous principal bundle $Q$ over a hermitian symmetric space $M=G/K$. The parameter space carries the structure of normal variety and has a canonical anti-holomorphic involution.…
We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators…
A general definition of a bimodule connection in noncommutative geometry has been recently proposed. For a given algebra this definition is compared with the ordinary definition of a connection on a left module over the associated…
The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizations, a significant class of…
Graded bundles are a particularly nice class of graded manifolds and represent a natural generalisation of vector bundles. By exploiting the formalism of supermanifolds to describe Lie algebroids we define the notion of a weighted…
A non associative, noncommutative algebra is defined that may be interpreted as a set of vector modules over a noncommutative surface of rotation. Two of these vector modules are identified with the analogues of the tangent and cotangent…
Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps…
In this note we highlight a common origin for many ubiquitous geometric structures, as well as several new ones by using only the functors of differential calculus in A.M Vinogradov's original sense, adapted to special classes of (graded)…
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played…
Connections on a trivial bundle MxG can be identified with their holonomy maps, i.e. with homomorphisms of a groupoid of paths in M into the gauge group G. For a connected compact G, various algebras depending on the set of the smooth…
Let E be a circle bundle over a Riemann surface that supports a contact structure transverse to the fibers. This paper presents a combinatorial definition of a differential graded algebra (DGA) that is an invariant of Legendrian knots in E.…
Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…
The characteristic forms in the bundle of connections of a principal bundle P over M determine the characteristic classes of P for degree less or equal to the dimension of M, and differential forms on the space of connections for higher…
We classify (possibly non commutative) algebras of low rank over a domain R. We first review results for algebras of rank 2 and for finite-dimensional division algebras over the real numbers. These results motivate us to consider which…
Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections to their geometric properties. Using this perspective, we generalize some classical results of Cartan and Nomizu to invariant…
In this paper we introduce a new invariant for a non-degenerate evolution algebra, which consists of an ordered sequence of evolution algebras of lower dimension, belonging all of them to a specific family. We use this invariant to propose…
We define and characterize spaces of manifold-valued generalized functions and generalized vector bundle homomorphisms in the setting of the full diffeomorphism-invariant vector-valued Colombeau algebra. Furthermore, we establish point…
This paper defines the concept of an oriented quantum algebra and develops its application to the construction of quantum link invariants. We show that all known quantum link invariants can be put into this framework.