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COHOMOLOGY OF THE VECTOR FIELDS LIE ALGEBRAS ON RP1 ACTING ON BILINEAR DIFFERENTIAL OPERATORS
Journal article   Peer reviewed

COHOMOLOGY OF THE VECTOR FIELDS LIE ALGEBRAS ON RP1 ACTING ON BILINEAR DIFFERENTIAL OPERATORS

Abdaoui Meher
Studia scientiarum mathematicarum Hungarica, Vol.56(3), pp.280-296
01/09/2019
DOI: https://doi.org/10.1556/012.2019.56.3.1433

Abstract

Mathematics Physical Sciences Science & Technology
Let Vect(RP1) be the Lie algebra of smooth vector fields on RP1. In this paper, we classify aff(1)-invariant linear differential operators from Vect(RP1) to D-lambda,D-mu;nu vanishing on aff(1), where D-lambda,D-mu;nu := Homdiff (F-lambda circle times F-mu; F-nu) is the space of bilinear differential operators acting on weighted densities. This result allows us to compute the first differential aff(1)relative cohomology of Vect(RP1) with coefficients in D-lambda,D-mu;nu.

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