Comment on the surface exponential for tensor fields

Starting from essentially commutative exponential map $E(B|I)$ for generic tensor-valued 2-forms $B$, introduced in [10] as direct generalization of the ordinary non-commutative $P$-exponent for 1-forms with values in matrices (i.e. in tensors of rank 2), we suggest a non-trivial but multi-parametric exponential $\mathcal E(B|I|t_\gamma)$, which can serve as an interesting multi-directional evolution operator in the case of higher ranks. To emphasize the most important aspects of the story, construction is restricted to backgrounds $I_{ijk}$, associated with the structure constants of commutative associative algebras, what makes it unsensitive to topology of the $2d$ surface. Boundary effects are also eliminated (straightfoward generalization is needed to incorporate them).