On the twisted Dorfman-Courant like brackets

• Autorzy: Mikulski Włodzimierz M.

Identyfikatory

DOI

10.7494/OpMath.2020.40.6.703

• Języki publikacji: EN

Abstrakty

EN

There are completely described all [formula]-gauge-natural operators C which, like to the Dorfman-Courant bracket, send closed linear 3-forms [formula]on a smooth (C ∞) vector bundle E into R-bilinear operators [formula] transforming pairs of linear sections of [formula] into linear sections of [formula]. Then all such C which also, like to the twisted Dorfman-Courant bracket, satisfy both some “restricted” condition and the Jacobi identity in Leibniz form are extracted.

Słowa kluczowe

EN

natural operator; linear vector field; linear form; (twisted) Dorfman-Courant bracket; Jacobi identity in Leibniz form

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2020
• Tom: Vol. 40, no. 6
• Strony: 703--723
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Mikulski Włodzimierz M.

• Jagiellonian University Department of Mathematics S. Łojasiewicza 6, Cracow, Poland

Bibliografia

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• [4] M. Gualtieri, Generalized complex geometry, Ann. of Math. 174 (2011) 1, 75-123.
• [5] N. Hitchin, Generalized Calabi-Yau manifolds, Q. J. Math. 54 (2003), 281-308.
• [6] M. Jotz Lean, C. Kirchhoff-Lukat, Natural lifts of Dorfman brackets, arXiv:1610.05986v2 [math.DG] 14 Jul 2017.
• [7] I. Kolar, P.W. Michor, J. Slovak, Natural Operations in Differential Geometry, Berlin, Germany Springer-Verlag, 1993.
• [8] Z.J. Liu, A. Weinstein, P. Xu, Main triples for Lie bialgebroids, J. Differ. Geom. 45 (1997), 547-574.
• [9] W.M. Mikulski, The natural operators similar to the twisted Courant bracket one, Mediter. J. Math. 16 (2019), Article no. 101.
• [10] W.M. Mikulski, The gauge-natural bilinear operators similar to the Dorfman-Courant bracket, Mediter. J. Math. 17 (2020), Article no. 40.
• [11] P. Severa, A. Weinstein, Poisson geometry with a 3-form background, Prog. Theor. Phys., Suppl. 144 (2001), 145-154.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020)