Modular classes of Loday algebroids

Mathieu Stiénon; Ping Xu

doi:10.1016/j.crma.2007.12.012

Modular classes of Loday algebroids

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Abstract

We introduce the concept of Loday algebroids, a generalization of Courant algebroids. We define the naive cohomology and modular class of a Loday algebroid, and we show that the modular class of the double of a Lie bialgebroid vanishes. For Courant algebroids, we describe the relation between the naive and standard cohomologies and we conjecture that they are isomorphic when the Courant algebroid is transitive. To cite this article: M. Stiénon, P. Xu, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Original language	English (US)
Pages (from-to)	193-198
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	346
Issue number	3-4
DOIs	https://doi.org/10.1016/j.crma.2007.12.012
State	Published - Feb 2008

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2007.12.012

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title = "Modular classes of Loday algebroids",

abstract = "We introduce the concept of Loday algebroids, a generalization of Courant algebroids. We define the naive cohomology and modular class of a Loday algebroid, and we show that the modular class of the double of a Lie bialgebroid vanishes. For Courant algebroids, we describe the relation between the naive and standard cohomologies and we conjecture that they are isomorphic when the Courant algebroid is transitive. To cite this article: M. Sti{\'e}non, P. Xu, C. R. Acad. Sci. Paris, Ser. I 346 (2008).",

author = "Mathieu Sti{\'e}non and Ping Xu",

note = "Funding Information: E-mail addresses: [email protected] (M. Sti{\'e}non), [email protected] (P. Xu). 1 Research supported by the European Union through the FP6 Marie Curie R.T.N. ENIGMA (Contract number MRTN-CT-2004-5652). 2 Research partially supported by NSF grant DMS-0605725 \& NSA grant H98230-06-1-0047.",

year = "2008",

month = feb,

doi = "10.1016/j.crma.2007.12.012",

language = "English (US)",

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pages = "193--198",

journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

number = "3-4",

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T1 - Modular classes of Loday algebroids

AU - Stiénon, Mathieu

AU - Xu, Ping

N1 - Funding Information: E-mail addresses: [email protected] (M. Stiénon), [email protected] (P. Xu). 1 Research supported by the European Union through the FP6 Marie Curie R.T.N. ENIGMA (Contract number MRTN-CT-2004-5652). 2 Research partially supported by NSF grant DMS-0605725 & NSA grant H98230-06-1-0047.

PY - 2008/2

Y1 - 2008/2

N2 - We introduce the concept of Loday algebroids, a generalization of Courant algebroids. We define the naive cohomology and modular class of a Loday algebroid, and we show that the modular class of the double of a Lie bialgebroid vanishes. For Courant algebroids, we describe the relation between the naive and standard cohomologies and we conjecture that they are isomorphic when the Courant algebroid is transitive. To cite this article: M. Stiénon, P. Xu, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

AB - We introduce the concept of Loday algebroids, a generalization of Courant algebroids. We define the naive cohomology and modular class of a Loday algebroid, and we show that the modular class of the double of a Lie bialgebroid vanishes. For Courant algebroids, we describe the relation between the naive and standard cohomologies and we conjecture that they are isomorphic when the Courant algebroid is transitive. To cite this article: M. Stiénon, P. Xu, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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U2 - 10.1016/j.crma.2007.12.012

DO - 10.1016/j.crma.2007.12.012

M3 - Article

AN - SCOPUS:39049136380

SN - 1631-073X

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EP - 198

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 3-4

ER -

Modular classes of Loday algebroids

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