The structure of F-tensorial cochains of differential operators

✍ Scribed by F.J. Bloore; G. Roberts

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 404 KB
• Volume: 10
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(99)00012-1

✦ Synopsis

Let M be a manifold. Let 3 = C"(M. Iw). Then the associative algebra ?) of differential operators on 3 is a two-sided 3-module. We prove that there is a natural isomorphism between the .3tensorial Hochschild p-cochains of 'D and the jets, taken on the diagonal, of smooth functions on the Cartesian product of p + 1 copies of M. There is an induced isomorphism of the corresponding associative differential graded algebras. The normalised 3-tensorial p-cochains correspond isomorphically to jets of those above functions which vanish on all the contiguous subdiagonals Xj+t = Xj. j = 0. p -I of AI"'+' '. This isomorphism may offer a useful alternative view of infinite-order jets of functions of several variables. taken on the diagonal as cochains of 'D,.