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The infinitesimal counterpart of tangent presymplectic groupoids of higher order
Archivum mathematicum, Tome 54 (2018) no. 3, pp. 135-151 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $.
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 $.
DOI : 10.5817/AM2018-3-135
Classification : 53C15, 53C75, 53D05
Keywords: IM-2 forms; complete lifts of vector fields and differential forms; twisted-Dirac structures; tangent functor of higher order; natural transformations 
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Kouotchop Wamba, P.M.; MBA, A. The infinitesimal counterpart of tangent presymplectic groupoids of higher order. Archivum mathematicum, Tome 54 (2018) no. 3, pp. 135-151. doi: 10.5817/AM2018-3-135

[1] Bursztyn, H., A., Cabrera: Multiplicative forms at the infinitesimal level. Math. Ann. 353 (2012), 663–705. | DOI | MR

[2] Bursztyn, H., Crainic, M., Weinstein, A., Zhu, C.: Integration of twisted Dirac bracket. Duke Math. J. 123 (2004), 549–607. | DOI | MR

[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

[4] Coste, A., Dazord, P., Weinstein, A.: Groupoïdes symplectiques. Publ. Dep. Math. Nouvelle Ser. A2, Univ. Claude-Bernard, Lyon 2 (1987), 1–62. | MR

[5] Courant, T.J.: Dirac manifolds. Trans. Amer. Math. Soc. 319 (1990), 631–661. | DOI | MR

[6] del Hoyo, M., Ortiz, C.: Morita equivalences of vector bundles. arXiv: 1612. 09289v2 [math. DG], 4 Apr. 2017, 2017. | MR

[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 | MR | Zbl

[8] Kolář, I., Michor, P., Slovák, J.: Natural operations in differential geometry. Springer-Verlag, 1993. | MR | Zbl

[9] Kouotchop Wamba, P.M., Ntyam, A.: Tangent lifts of higher order of multiplicative Dirac structures. Arch. Math. (Brno) 49 (2013), 87–104. | DOI | MR

[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

[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

[12] Mackenzie, K.: On symplectic double groupoids and the duality of Poisson groupoids. Internat. J. Math. 10 (1999), 435–456. | DOI | MR

[13] Mackenzie, K.: Theory of Lie groupoids and Lie algebroids. London Math. Soc. Lecture Note Ser. 213 (2005). | MR

[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 | MR

[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

[16] Vaisman, I.: Lectures on the geometry of Poisson manifolds. vol. 118, Progress in Math., Birkhäuser, 1994. | MR | Zbl

[17] Wouafo Kamga, J.: On the tangential linearization of Hamiltonian systems. International Centre for Theoretical Physics, Trieste, 1997.

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