Involutive distributions of operator-valued evolutionary vector fields and their affine geometry. II

We generalize the notion of a Lie algebroid over infinite jet bundle by replacing the variational anchor with an N-tuple of differential operators whose images in the Lie algebra of evolutionary vector fields of the jet space are subject to collective commutation closure. The linear space of such operators becomes an algebra with bi-differential structural constants, of which we study the canonical structure. In particular, we show that these constants incorporate bi-differential analogues of Christoffel symbols.

💡 Research Summary

The paper extends the classical notion of a Lie algebroid over an infinite jet bundle by replacing the single variational anchor with an N‑tuple of differential operators. Each operator (A_i) maps sections of a vector bundle into evolutionary vector fields on the jet space, and the crucial hypothesis is that the images of all (A_i) together form an involutive distribution: for any sections (p,q) and any pair of indices (i,j) the commutator (