{
"id": "1709.03973",
"version": "v1",
"published": "2017-09-12T17:57:38.000Z",
"updated": "2017-09-12T17:57:38.000Z",
"title": "Duality for Differential Operators of Lie-Rinehart Algebras",
"authors": [
"Thierry Lambre",
"Patrick Le Meur"
],
"categories": [
"math.RA",
"math.KT",
"math.QA"
],
"abstract": "Let (S,L) be a Lie-Rinehart algebra over a commutative ring R. This article proves that, if S is flat as an R-module and has Van den Bergh duality in dimension n, and if L is finitely generated and projective with constant rank d as an S-module, then the enveloping algebra of (S,L) has Van den Bergh duality in dimension n+d. When, moreover, S is Calabi-Yau and the d-th exterior power of L is free over S, the article proves that the enveloping algebra is skew-Calabi-Yau, and it describes a Nakayama automorphism of it. These considerations are specialised to Poisson enveloping algebras. They are also illustrated on Poisson structures over two and three dimensional polynomial algebras and on Nambu-Poisson structures on certain two dimensional hypersurfaces.",
"revisions": [
{
"version": "v1",
"updated": "2017-09-12T17:57:38.000Z"
}
],
"analyses": {
"subjects": [
"16E65",
"16E40",
"16S32",
"16W25",
"17B63",
"17B66"
],
"keywords": [
"lie-rinehart algebra",
"van den bergh duality",
"differential operators",
"enveloping algebra",
"d-th exterior power"
],
"note": {
"typesetting": "TeX",
"pages": 0,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}