Involutive distributions of operator-valued evolutionary vector fields and their affine geometry. II
Mathematical Physics
2011-04-19 v3 Differential Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
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.
Cite
@article{arxiv.0904.1555,
title = {Involutive distributions of operator-valued evolutionary vector fields and their affine geometry. II},
author = {Arthemy V. Kiselev and Johan W. van de Leur},
journal= {arXiv preprint arXiv:0904.1555},
year = {2011}
}
Comments
10 pages