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

A.V. Kiselev, J.W. van de Leur

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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.
Original languageEnglish
Title of host publicationSummetríâ V : the 5th international workshop in Group Analysis of Differential Equations and Integrable Systems
Publication statusPublished - 6 Jun 2010

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