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IM-2 forms; complete lifts of vector fields and differential forms; twisted-Dirac structures; tangent functor of higher order; natural transformations
Let $\left(G, \omega \right)$ be a presymplectic groupoid. In this paper we characterize the infinitesimal counter part of the tangent presymplectic groupoid of higher order, $(T^{r}G, \omega ^{\left(c\right)})$ where $T^{r}G$ is the tangent groupoid of higher order and $\omega ^{\left(c\right)}$ is the complete lift of higher order of presymplectic form $\omega $.
[1] Bursztyn, H., A., Cabrera: Multiplicative forms at the infinitesimal level. Math. Ann. 353 (2012), 663–705. DOI 10.1007/s00208-011-0697-5 | MR 2923945
[2] Bursztyn, H., Crainic, M., Weinstein, A., Zhu, C.: Integration of twisted Dirac bracket. Duke Math. J. 123 (2004), 549–607. DOI 10.1215/S0012-7094-04-12335-8 | MR 2068969
[3] Cantrijn, F., Crampin, M., Sarlet, W., Saunders, D.: The canonical isomorphism between $T^{k}T^{\ast }$ and $T^{\ast }T^{k}$. C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), 1509–1514. MR 1033091
[4] Coste, A., Dazord, P., Weinstein, A.: Groupoïdes symplectiques. Publ. Dep. Math. Nouvelle Ser. A2, Univ. Claude-Bernard, Lyon 2 (1987), 1–62. MR 0996653
[5] Courant, T.J.: Dirac manifolds. Trans. Amer. Math. Soc. 319 (1990), 631–661. DOI 10.1090/S0002-9947-1990-0998124-1 | MR 0998124
[6] del Hoyo, M., Ortiz, C.: Morita equivalences of vector bundles. arXiv: 1612. 09289v2 [math. DG], 4 Apr. 2017, 2017. MR 3679884
[7] Gancarzewicz, J., Mikulski, W., Pogoda, Z.: Lifts of some tensor fields and connections to product preserving functors. Nagoya Math. J. 135 (1994), 1–41. DOI 10.1017/S0027763000004931 | MR 1295815 | Zbl 0813.53010
[8] Kolář, I., Michor, P., Slovák, J.: Natural operations in differential geometry. Springer-Verlag, 1993. MR 1202431 | Zbl 0782.53013
[9] Kouotchop Wamba, P.M., Ntyam, A.: Tangent lifts of higher order of multiplicative Dirac structures. Arch. Math. (Brno) 49 (2013), 87–104. DOI 10.5817/AM2013-2-87 | MR 3118866
[10] Kouotchop Wamba, P.M., Ntyam, A., Wouafo Kamga, J.: Some properties of tangent Dirac structures of higher order. Arch. Math. (Brno) 48 (2012), 17–22. MR 2813543
[11] Kouotchop Wamba, P.M., Ntyam, A., Wouafo Kamga, J.: Tangent lift of higher order of multivector fields and applications. J. Math. Sci. Adv. Appl. 15 (2012), 89–112. MR 3058846
[12] Mackenzie, K.: On symplectic double groupoids and the duality of Poisson groupoids. Internat. J. Math. 10 (1999), 435–456. DOI 10.1142/S0129167X99000185 | MR 1697617
[13] Mackenzie, K.: Theory of Lie groupoids and Lie algebroids. London Math. Soc. Lecture Note Ser. 213 (2005). MR 2157566
[14] Morimoto, A.: Lifting of some type of tensors fields and connections to tangent bundles of $p^{r}$-velocities. Nagoya Math. J. 40 (1970), 13–31. DOI 10.1017/S0027763000013830 | MR 0279720
[15] Ortiz, C.: B-field transformations of Poisson groupoids. Proceedings of the Second Latin Congress on Symmetries in Geometry and Physics, Matemática Contemporânea, vol. 41, 2012, pp. 113–148. MR 3087576
[16] Vaisman, I.: Lectures on the geometry of Poisson manifolds. vol. 118, Progress in Math., Birkhäuser, 1994. MR 1269545 | Zbl 0810.53019
[17] Wouafo Kamga, J.: On the tangential linearization of Hamiltonian systems. International Centre for Theoretical Physics, Trieste, 1997.
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