## 13 Citations

### Holomorphic string algebroids

- MathematicsTransactions of the American Mathematical Society
- 2020

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…

### On Dorfman connections of a Courant algebroid

- Mathematics
- 2020

We extend the Courant-Dorfman algebra of a Courant algebroid E to an algebra of differential operators on tensor products of E with values in tensor bundles of a vector bundle B, predual of E.…

### The standard cohomology of regular Courant algebroids

- Mathematics
- 2021

For any Courant algebroid E over a smooth manifold M with characteristic distribution F which is regular, we study the standard cohomology H• st(E) by using a special spectral sequence. We prove a…

### Atiyah class of a Manin pair

- Mathematics
- 2020

A Courant algebroid $E$ with a Dirac structure $L\subset E$ is said to be a Manin pair. We first discuss $E$-Dorfman connections on predual vector bundles $B$ and develop the corresponding Cartan…

### Dirac groupoids and Dirac bialgebroids

- MathematicsJournal of Symplectic Geometry
- 2019

We describe infinitesimally Dirac groupoids via geometric objects that we call Dirac bialgebroids. In the two well-understood special cases of Poisson and presymplectic groupoids, the Dirac…

### Linear generalised complex structures.

- Mathematics
- 2020

This paper studies linear generalised complex structures over vector bundles, as a generalised geometry version of holomorphic vector bundles. In an adapted linear splitting, a linear generalised…

### DIRAC ACTIONS AND LU’S LIE ALGEBROID

- Mathematics
- 2014

Poisson actions of Poisson Lie groups have an interesting and rich geometric structure. We will generalize some of this structure to Dirac actions of Dirac Lie groups. Among other things, we extend a…

### Canonical metrics on holomorphic Courant algebroids

- MathematicsProceedings of the London Mathematical Society
- 2022

The solution of the Calabi Conjecture by Yau implies that every Kähler Calabi–Yau manifold X$X$ admits a metric with holonomy contained in SU(n)$\mathrm{SU}(n)$ , and that these metrics are…

### Gauge theory for string algebroids

- Mathematics
- 2020

We introduce a moment map picture for holomorphic string algebroids where the Hamiltonian gauge action is described by means of Morita equivalences, as suggested by higher gauge theory. The zero…

## References

SHOWING 1-10 OF 19 REFERENCES

### Matched pairs of Lie algebroids

- MathematicsGlasgow Mathematical Journal
- 1997

Abstract We extend to Lie algebroids the notion variously known as a double Lie algebra (Lu and Weinstein), matched pair of Lie algebras (Majid), or twilled extension of Lie algebras…

### A construction of Courant algebroids on foliated manifolds

- Mathematics
- 2010

For any transversal-Courant algebroid E on a foliated manifold (M,F), and for any choice of a decomposition T M = TF © Q, we construct a

### On Regular Courant Algebroids

- Mathematics
- 2009

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…

### Courant algebroids, derived brackets and even symplectic supermanifolds

- Mathematics
- 1999

In this dissertation we study Courant algebroids, objects that first appeared in the work of T. Courant on Dirac structures; they were later studied by Liu, Weinstein and Xu who used Courant…

### Remarks on the Definition of a Courant Algebroid

- Mathematics
- 2002

The notion of a Courant algebroid was introduced by Liu, Weinstein, and Xu in 1997. Its definition consists of five axioms and a defining relation for a derivation. It is shown that two of the axioms…

### MATCHED PAIRS OF LIE GROUPS ASSOCIATED TO SOLUTIONS OF THE YANG-BAXTER EQUATIONS

- Mathematics
- 1990

Two groups G, H are said to be a matched pair if they act on each other and these actions, (a, /?), obey a certain compatibility condition. In such a situation one may form a bicrossproduct group,…

### Manin Triples for Lie Bialgebroids

- Mathematics
- 1995

In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does…

### Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids

- Mathematics
- 2010

We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson…