Tangent lifts of higher order of multiplicative Dirac structures. (English) Zbl 1299.53088

Kouotchop Wamba, P. M.; Ntyam, A.

Arch. Math., Brno 49, No. 2, 87-104 (2013).

The authors continue their previous research, jointly with J. Wouafo Kamga, on higher-order Dirac and Poisson structures [Arch. Math., Brno 47, No. 1, 17–22 (2011; Zbl 1240.53058); J. Math. Sci. Adv. Appl. 15, No. 1, 13–36 (2012; Zbl 1263.53077); Arch. Math., Brno 48, No. 3, 233–241 (2012; Zbl 1274.53052)]. In the present paper, they study the tangent lifts of higher order of multiplicative Dirac structures and they describe the Lie bialgebroid structures and the algebroid-Dirac structures induced by these prolongations.

Reviewer: Ivan Kolář (Brno)

MSC:

53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C75	Geometric orders, order geometry
53D05	Symplectic manifolds (general theory)

Keywords:

Lie groupoids; Lie bialgebroids; multiplicative Dirac structures; tangent functor of higher order; natural transformations

Citations:

Zbl 1240.53058; Zbl 1263.53077; Zbl 1274.53052