Related papers: String principal bundles and Courant algebroids
We introduce the category of holomorphic string algebroids, whose objects are Courant extensions of Atiyah Lie algebroids of holomorphic principal bundles, as considered by Bressler, and whose morphisms correspond to inner morphisms of the…
In this paper, a notion of a principal $2$-bundle over a Lie groupoid has been introduced. For such principal $2$-bundles, we produced a short exact sequence of VB-groupoids, namely, the Atiyah sequence. Two notions of connection structures…
We express any Courant algebroid bracket by means of a metric connection, and construct a Courant algebroid structure on any orthogonal Whitney sum $E\oplus C$ where E is a given Courant algebroid and C is a flat, pseudo- Euclidean vector…
In categorified symplectic geometry, one studies the categorified algebraic and geometric structures that naturally arise on manifolds equipped with a closed nondegenerate (n+1)-form. The case relevant to classical string theory is when n=2…
We introduce the Courant algebroid lift, a new construction that takes a Courant algebroid together with a vector bundle connection and produces, when the connection is flat in the image of the anchor, a Courant algebroid. In general, this…
Inspired by recent works of Zang Liu, Alan Weinstein and Ping Xu, we introduce the notions of CC algebroids and non asymmetric Courant algebroids and study these structures. It is shown that CC algebroids of rank greater than 3 are the same…
We introduce the notion of \textbf{Q}-principal bundle, which is the appropriate version of principal fibre bundles in the setting of R. Barre's \textbf{Q}-manifolds. As an application, we prove that every transitive Lie algebroid arises…
In \cite{Bi2} (Canad. Jour. Math. Vol. 58) we defined connections on a parabolic principal bundle. While connections on usual principal bundles are defined as splittings of the Atiyah exact sequence, it was noted in \cite{Bi2} that the…
We investigate principal bundles over a root stack. In case of dimension one, we generalize the criterion of Weil and Atiyah for a principal bundle to have an algebraic connection.
We investigate Atiyah algebroids, i.e. the infinitesimal objects of principal bundles, from the viewpoint of Lie algebraic approach to space. First we show that if the Lie algebras of smooth sections of two Atiyah algebroids are isomorphic,…
We introduce conformal Courant algebroids, a mild generalization of Courant algebroids in which only a conformal structure rather than a bilinear form is assumed. We introduce exact conformal Courant algebroids and show they are classified…
To address the need for a unified framework that incorporates Lie algebroid connections on both vector and principal bundles, this paper investigates a generalized Atiyah algebroid structure and its short exact sequence. Building on this…
We consider stable and semistable principal bundles over a smooth projective real algebraic curve, equipped with a real or pseudo-real structure in the sense of Atiyah. After fixing suitable topological invariants, one can build a suitable…
We present a derivation-based Atiyah sequence for noncommutative principal bundles. Along the way we treat the problem of deciding when a given $^*$-automorphism on the quantum base space lifts to a $^*$-automorphism on the quantum total…
Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the direct sum of tangent and cotangent bundles with the bracket introduced by T. Courant for the study of Dirac structures. Within the category…
Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing…
We investigate an interplay between some ideas in traditional gauge theory and certain concepts in fibered categories. We accomplish this by introducing a notion of a principal Lie 2-group bundle over a Lie groupoid and studying its…
The core diagram of a double Lie algebroid consists in the core of the double Lie algebroid, together with the two core-anchor maps to the sides of the double Lie algebroid. If these two core anchors are surjective, then the double Lie…
A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is…
In this paper we show how connections and their generalizations on transitive Lie algebroids are related to the notion of connections in the framework of the derivation-based noncommutative geometry. In order to compare the two…