TY - JOUR
T1 - VB-Courant algebroids, E-Courant algebroids and generalized geometry
AU - Lang, Honglei
AU - Sheng, Yunhe
AU - Wade, Aïssa
N1 - Publisher Copyright:
© Canadian Mathematical Society 2018.
PY - 2018/9
Y1 - 2018/9
N2 - In this paper, we first discuss the relation between VB-Courant algebroids and E-Courant algebroids, and we construct some examples of E-Courant algebroids. Then we introduce the notion of a generalized complex structure on an E-Courant algebroid, unifying the usual generalized complex structures on even-dimensional manifolds and generalized contact structures on odddimensional 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 gl(V) ⊕ V correspond to complex Lie algebra structures on V.
AB - In this paper, we first discuss the relation between VB-Courant algebroids and E-Courant algebroids, and we construct some examples of E-Courant algebroids. Then we introduce the notion of a generalized complex structure on an E-Courant algebroid, unifying the usual generalized complex structures on even-dimensional manifolds and generalized contact structures on odddimensional 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 gl(V) ⊕ V correspond to complex Lie algebra structures on V.
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U2 - 10.4153/CMB-2017-079-7
DO - 10.4153/CMB-2017-079-7
M3 - Article
AN - SCOPUS:85050373503
SN - 0008-4395
VL - 61
SP - 588
EP - 607
JO - Canadian Mathematical Bulletin
JF - Canadian Mathematical Bulletin
IS - 3
ER -