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Graded Jacobi operators on the algebra of differential forms

Published online by Cambridge University Press:  04 December 2007

J. V. BELTRÁN ,
J. MONTERDE  and
O. A. SÁNCHEZ-VALENZUELA
J. V. BELTRÁN
Affiliation:
Dpt. de Geometria i Topologia, Universitatt de València; C/Dr. Moliner 50, E-46100-Burjassot (València), Spain. e-mail address: beltranv@uv.es
J. MONTERDE
Affiliation:
Dpt. de Geometria i Topologia, Universitatt de València; C/Dr. Moliner 50, E-46100-Burjassot (València), Spain. e-mail address: monterde@uv.es
O. A. SÁNCHEZ-VALENZUELA
Affiliation:
CIMAT; Apdo. Postal, 402; C.P. 36000 Guanajuato, Gto., México. e-mail address: sanchez@uv.es Dpt. de Geometria i Topologia, Universitatt de València; C/Dr. Moliner 50, E-46100-Burjassot (València), Spain.
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Abstract

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One-to-one correspondences are established between the set of all nondegenerate graded Jacobi operators of degree $-1$ defined on the graded algebra $\Omega(M)$ of differential forms on a smooth, oriented, Riemannian manifold $M$, the space of bundle isomorphisms $L{\A}TM{\to} TM$, and the space of nondegenerate derivations of degree $1$ having null square. Derivations with this property, and Jacobi structures of odd $\Bbb Z_2$-degree are also studied through the action of the automorphism group of $\Omega(M)$.

Keywords

differential formsgraded Poisson bracketsgraded symplectic formsJacobi structures
Type
Research Article
Information
Compositio Mathematica , Volume 106 , Issue 1 , March 1997 , pp. 43 - 59
Copyright
© 1997 Kluwer Academic Publishers