CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

$\mathsf{VB}$-Courant algebroids, $\mathsf{E}$-Courant algebroids and generalized geometry

  • Honglei Lang,
    Max Planck Institute for Mathematics, Bonn D-53111, Germany
  • Yunhe Sheng,
    Department of Mathematics, Jilin University, Chanchung, 130012, Jilin, China
  • Aissa Wade,
    Mathematics Department, Penn State University, University Park, Pennsylvania 16802, USA
Format:   LaTeX   MathJax   PDF  

Abstract

In this paper, we first discuss the relation between $\mathsf{VB}$-Courant algebroids and $\mathsf{E}$-Courant algebroids and construct some examples of $\mathsf{E}$-Courant algebroids. Then we introduce the notion of a generalized complex structure on an $\mathsf{E}$-Courant algebroid, unifying the usual generalized complex structures on even-dimensional manifolds and generalized contact structures on odd-dimensional manifolds. Moreover, we study generalized complex structures on an omni-Lie algebroid in detail. In particular, we show that generalized complex structures on an omni-Lie algebra $\operatorname{gl}(V)\oplus V$ correspond to complex Lie algebra structures on $V$.
Keywords: $\mathsf{VB}$-Courant algebroid, $\mathsf{E}$-Courant algebroid, omni-Lie algebroid, generalized complex structure, algebroid-Nijenhuis structure $\mathsf{VB}$-Courant algebroid, $\mathsf{E}$-Courant algebroid, omni-Lie algebroid, generalized complex structure, algebroid-Nijenhuis structure
MSC Classifications: 53D17, 18B40, 58H05 show english descriptions Poisson manifolds; Poisson groupoids and algebroids
Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]
Pseudogroups and differentiable groupoids [See also 22A22, 22E65]
53D17 - Poisson manifolds; Poisson groupoids and algebroids
18B40 - Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]
58H05 - Pseudogroups and differentiable groupoids [See also 22A22, 22E65]
 

© Canadian Mathematical Society, 2018 : https://cms.math.ca/