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

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

2009-04-09

arxiv.org/abs/0904.1555v3

Proc. 5th Int. workshop `Group analysis of differential equations and integrable systems' (June 6-10, 2010; Protaras, Gyprus),

Physics

Mathematical Physics

10 pages

Scientific paper

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.

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