Generalized n-omni-Lie Algebroids

In this paper, we report the structure of generalized n-omni-Lie algebroids. Firstly, the definitions of a \mathfrakD^n - 1E -value pairing and a higher Dorfman bracket are given on the direct sum bundle \mathfrakD_0^nE \oplus \mathfrakJE . The generalized n-omni-Lie algebroids are constructed and their properties are proved and similar to those of n-omni-Lie algebroids. Secondly, when E is a trivial line bundle, a higher Dorfman bracket is constructed on the section \Gamma \left( \varepsilon ^n \right) to obtain the generalized n-omni-Lie algebroids \mathcalE^n(M \times \mathbbR) associated to a trivial line bundle M \times \mathbbR Finally, the higher Dirac structure of the generalized n-omni-Lie algebroid is presented, and the graph Gr(B_\Delta ) is verified as the higher Dirac structure of generalized n-omni-Lie algebroids.