Letters in Mathematical Physics

, volume 69 , issue 1-3 , pages 61-87

Derived Brackets

YVETTE KOSMANN-SCHWARZBACH ¹

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Centre de Mathématiques, UMR 7640 du CNRS, École Polytechnique, Palaiseau, France |

Publication type: Journal Article

Publication date: 2004-07-01

Springer Nature

Letters in Mathematical Physics

scimago Q2

wos Q3

SJR: 0.892

CiteScore: 2.6

Impact factor: 1.4

ISSN: 03779017, 15730530

DOI: 10.1007/s11005-004-0608-8

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Statistical and Nonlinear Physics

Mathematical Physics

Abstract

We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and of Vinogradov, and we prove that the Vinogradov bracket is the skew-symmetrization of a derived bracket. Odd (resp., even) Poisson brackets on supermanifolds are derived brackets of canonical even (resp., odd) Poisson brackets on their cotangent bundle (resp., parity-reversed cotangent bundle). Lie algebras have analogous properties, and the theory of Lie algebroids unifies the results valid for manifolds on the one hand, and for Lie algebras on the other. We outline the role of derived brackets in the theory of ‘Poisson structures with background’.

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GOST |

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GOST Copy

KOSMANN-SCHWARZBACH Y. Derived Brackets // Letters in Mathematical Physics. 2004. Vol. 69. No. 1-3. pp. 61-87.

GOST all authors (up to 50) Copy

KOSMANN-SCHWARZBACH Y. Derived Brackets // Letters in Mathematical Physics. 2004. Vol. 69. No. 1-3. pp. 61-87.

RIS |

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RIS Copy

TY - JOUR

DO - 10.1007/s11005-004-0608-8

UR - https://doi.org/10.1007/s11005-004-0608-8

TI - Derived Brackets

T2 - Letters in Mathematical Physics

AU - KOSMANN-SCHWARZBACH, YVETTE

PY - 2004

DA - 2004/07/01

PB - Springer Nature

SP - 61-87

IS - 1-3

VL - 69

SN - 0377-9017

SN - 1573-0530

ER -

BibTex |

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BibTex (up to 50 authors) Copy

@article{2004_KOSMANN-SCHWARZBACH,

author = {YVETTE KOSMANN-SCHWARZBACH},

title = {Derived Brackets},

journal = {Letters in Mathematical Physics},

year = {2004},

volume = {69},

publisher = {Springer Nature},

month = {jul},

url = {https://doi.org/10.1007/s11005-004-0608-8},

number = {1-3},

pages = {61--87},

doi = {10.1007/s11005-004-0608-8}

}

MLA

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MLA Copy

KOSMANN-SCHWARZBACH, YVETTE. “Derived Brackets.” Letters in Mathematical Physics, vol. 69, no. 1-3, Jul. 2004, pp. 61-87. https://doi.org/10.1007/s11005-004-0608-8.

Publisher

Springer Nature

Journal

Letters in Mathematical Physics

scimago Q2

wos Q3

SJR

0.892

CiteScore

2.6

Impact factor

1.4

ISSN

03779017 (Print)

15730530 (Electronic)