On linear Dirac structures of order p /spl les/ 7

The examination of Nambu-Poisson structures has resulted into the introduction of the higher analogues of linear Dirac structures [W. Aissa et al.]. To make the pair define the linear Dirac structure of order p, it is required that the p-form Omega satisfied condition (H) from paragraph 2. We show that in the case 3 les p les dimU les 7 condition (H) is equal to decomposability Omega. Thus, in small dimensions condition (H) might be considered as criteria of decomposability of p-form different from quadratic criterions of decomposability similar to Plucker´s criterions