On the gauge-natural operators similar to the twisted Dorfman-Courant bracket

• Autorzy: Mikulski Włodzimierz M.

Identyfikatory

DOI

10.7494/OpMath.2021.41.2.205

• Języki publikacji: EN

Abstrakty

EN

All [formula]-gauge-natural operators C sending linear 3-forms [formula] on a smooth [formula] vector bundle E into R-bilinear operators [formula] transforming pairs of linear sections of [formula] into linear sections of [formula] are completely described. The complete descriptions is given of all generalized twisted Dorfman-Courant brackets C (i.e. C as above such that C0 is the Dorfman-Courant bracket) satisfying the Jacobi identity for closed linear 3-forms H . An interesting natural characterization of the (usual) twisted Dorfman-Courant bracket is presented.

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: 2021
• Tom: Vol. 41, no. 2
• Strony: 205--226
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Mikulski Włodzimierz M.

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

• https://orcid.org/0000-0002-2905-0461

Bibliografia

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• [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, Springer-Verlag, Berlin, 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] W.M. Mikulski, On the twisted Dorfman-Courant like brackets, Opuscula Math. 40 (2020), no. 6, 703-723.
• [12] P. Severa, A. Weinstein, Poisson geometry with a 3-form background, Prog. Theor. Phys., Suppl. (2001), 145-154.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).