Comment on the surface exponential for tensor fields

Starting from an essentially commutative exponential map E(B|I) for generic tensor-valued 2-forms B, which were introduced in [10] as a direct generalization of the ordinary noncommutative P exponent for 1 forms with values in matrices (i.e., in tensors of rank 2), we suggest a nontrivial but multiparametric exponential E(B|I|t_γ), which can serve as an interesting multidirectional evolution operator in the case of higher ranks. To emphasize the most important aspects of the article, the construction is restricted to the backgrounds I _ijk , which are associated with the structure constants of the commutative associative algebras, which make it insensitive to the topology of the 2D surface. Boundary effects are also eliminated (straightforward generalization is needed to incorporate them).