相关论文: Anchored vector bundles and algebroids

In this letter we investigate some aspects of the noncommutative differential geometry based on derivations of the algebra of endomorphisms of an oriented complex hermitian vector bundle. We relate it, in a natural way, to the geometry of…

We associate a real distribution to any complex Lie algebroid that we call distribution of real elements and a new invariant that we call real rank, given by the pointwise rank of this distribution. When the real rank is constant, we obtain…

The purpose of this article is to show that the bivariant algebraic $A$-cobordism groups considered previously by the author are independent of the chosen base ring $A$. This result is proven by analyzing the bivariant ideal generated by…

We introduce Courant 1-derivations, which describe a compatibility between Courant algebroids and linear (1,1)-tensor fields and lead to the notion of Courant-Nijenhuis algebroids. We provide examples of Courant 1-derivations on exact…

A plane curve C defined by a homogeneous polynomial satisfying Laplace's equation appears canonically as the vanishing of the Pfaffian of a skew-symmetric matrix of linear forms. As a consequence there is a natural semi-stable rank two…

Courant algebroids are a natural generalization of quadratic Lie algebras, appearing in various contexts in mathematical physics. A connection on a Courant algebroid gives an analogue of a covariant derivative compatible with a given…

In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle $TM\oplus\wedge^nT^*M$ for an $m$-dimensional manifold. As an application, we revisit Nambu-Poisson structures…

For any regular Courant algebroid, we construct a characteristic class a la Chern-Weil. This intrinsic invariant of the Courant algebroid is a degree-3 class in its naive cohomology. When the Courant algebroid is exact, it reduces to the…

The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold has an almost…

We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential satisfies a formula that is formally identical to the Cartan…

We construct a generalization of Courant algebroids which are classified by the third cohomology group $H^3(A,V)$, where $A$ is a Lie Algebroid, and $V$ is an $A$-module. We see that both Courant algebroids and $\mathcal{E}^1(M)$ structures…

Motivated by the classical theory of spin structures, we develop a theory for lifting free C$^*$-dynamical systems, a.k.a. noncommutative principal bundles, along central extensions. This theory extends the bundle-theoretic notion of spin…

Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as canonical examples. We present and study the concept of the linearisation of graded…

We introduce the notion of matched pairs of Courant algebroids and give several examples arising naturally from complex manifolds, holomorphic Courant algebroids, and certain regular Courant algebroids. We consider the matched sum of two…

The notion of a \emph{higher-order algebroid}, as introduced by J\'o\'zwikowski and Rotkiewicz in their work \emph{Higher-order analogs of Lie algebroids via vector bundle comorphisms} (SIGMA, 2018), generalizes the concepts of a…

Clifford indices of vector bundles on algebraic curves were introduced in a previous paper of the authors. In this paper we study bundles of rank 2 which compute these Clifford indices. This is of particular interest in the light of…

Using an explicit resolution of the diagonal for the variety V_5, we provide cohomological characterizations of the universal and quotient bundles. A splitting criterion for bundles over V_5 is also proved. The presentation of semistable…

A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of…

Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such…

Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also constructed abstractly starting from an arbitrary almost Lie…