On higher dimensional exact Courant algebroids

Rengifo, Camilo

doi:10.1016/j.geomphys.2016.04.015

Cited by 2 publications

(3 citation statements)

References 13 publications

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“…The conditions for F to define an L ∞ -morphism (see eq. ( 55) and (56) in Remark A.12) coincide with the last two compatibility conditions (25) and (26). Finally F 1 and F 2 are clearly C ∞ (M )-linear.…”

Section: 2supporting

confidence: 63%

“…Lie bracket, the Maurer-Cartan equation reads Dα − 1 2 [α, α] = 0, where the minus signs comes from the décalage isomorphisms. It is easily seen that all the results of this section hold replacing 26 T M with any Lie algebroid A over M .…”

Section: Maurer-cartan Elementsmentioning

confidence: 86%

“…Further, a preliminary computation indicates that the Courant algebroid structure can be recovered from the R[2]-principal bundle in a way parallel to the case of exact Courant algebroids. (See [26,Ex. 5.7] for the exact case, where Rengifo takes derived brackets of Q with invariant vector fields on the R[2]-principal bundle, i.e.…”

Section: R[2]mentioning

confidence: 99%

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L∞-actions of Lie algebroids

Brahic¹,

Zambon

2021

Commun. Contemp. Math.

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We consider homotopy actions of a Lie algebroid on a graded manifold, defined as suitable [Formula: see text]-algebra morphisms. On the “semi-direct product” we construct a homological vector field that projects to the Lie algebroid. Our main theorem states that this construction is a bijection. Since several classical geometric structures can be described by homological vector fields as above, we can display many explicit examples, involving Lie algebroids (including extensions, representations up to homotopy and their cocycles) as well as transitive Courant algebroids.

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Section: 2supporting

confidence: 63%

Section: Maurer-cartan Elementsmentioning

confidence: 86%