{
  "id": "2105.15019",
  "version": "v1",
  "published": "2021-05-31T14:59:47.000Z",
  "updated": "2021-05-31T14:59:47.000Z",
  "title": "The Standard cohomology of regular Courant algebroids",
  "authors": [
    "Xiongwei Cai",
    "Zhuo Chen",
    "Maosong Xiang"
  ],
  "comment": "29 pages",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For any Courant algebroid $E$ over a smooth manifold $M$ with characteristic distribution $F$ which is regular, we study the standard cohomology $H^\\bullet_{\\operatorname{st}}(E)$ by using a special spectral sequence. We prove a theorem which tells how a natural transgression map $[\\mathcal{T}]$ together with the Chevalley-Eilenberg cohomology of the ample Lie algebroid $A_E$ of $E$ with coefficient in the symmetric tensor product ${S(TM/F)}$ of the normal bundle $TM/F$ determines $H^\\bullet_{\\operatorname{st}}(E)$, thereby significantly reducing the range of generators of the standard cohomology. We can also recover an earlier result by Ginot and Grutzmann (J.Symplectic Geom.7(2009), no.3, 311-335) in the situation that the base manifold $M$ splits. In addition, we apply the theorem to two special types of regular Courant algebroids: generalized exact ones and those arising from regular Lie algebroids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-31T14:59:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58A50",
      "53D17",
      "16E45"
    ],
    "keywords": [
      "regular courant algebroids",
      "standard cohomology",
      "regular lie algebroids",
      "symmetric tensor product",
      "natural transgression map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}