Ternary invariant differential operators acting on spaces of weighted densities

Research output: Contribution to journalArticle

Abstract

We classify ternary differential operators over n-dimensional manifolds. These operators act on the spaces of weighted densities and are invariant with respect to the Lie algebra of vector fields. For n = 1, some of these operators can be expressed in terms of the de Rham exterior differential, the Poisson bracket, the Grozman operator, and the Feigin-Fuchs antisymmetric operators; four of the operators are new up to dualizations and permutations. For n > 1, we list multidimensional conformal tranvectors, i.e., operators acting on the spaces of weighted densities and invariant with respect to o(p + 1, q + 1), where p + q = n. With the exception of the scalar operator, these conformally invariant operators are not invariant with respect to the whole Lie algebra of vector fields.

Original languageEnglish (US)
Pages (from-to)137-150
Number of pages14
JournalTheoretical and Mathematical Physics
Volume158
Issue number2
DOIs
StatePublished - Feb 1 2009

Fingerprint

Invariant Differential Operators
differential operators
Ternary
operators
Operator
Invariant
Vector Field
Lie Algebra
algebra
Dualization
Invariant Operator
Poisson Bracket
Antisymmetric
permutations
Exception
brackets
Differential operator
n-dimensional
lists
Permutation

Keywords

  • Conformal structure
  • Density tensor
  • Invariant operator
  • Transvector

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Ternary invariant differential operators acting on spaces of weighted densities. / Bouarroudj, Sofiane.

In: Theoretical and Mathematical Physics, Vol. 158, No. 2, 01.02.2009, p. 137-150.

Research output: Contribution to journalArticle

@article{529893973d834e7aa9e1425b984c39e0,
title = "Ternary invariant differential operators acting on spaces of weighted densities",
abstract = "We classify ternary differential operators over n-dimensional manifolds. These operators act on the spaces of weighted densities and are invariant with respect to the Lie algebra of vector fields. For n = 1, some of these operators can be expressed in terms of the de Rham exterior differential, the Poisson bracket, the Grozman operator, and the Feigin-Fuchs antisymmetric operators; four of the operators are new up to dualizations and permutations. For n > 1, we list multidimensional conformal tranvectors, i.e., operators acting on the spaces of weighted densities and invariant with respect to o(p + 1, q + 1), where p + q = n. With the exception of the scalar operator, these conformally invariant operators are not invariant with respect to the whole Lie algebra of vector fields.",
keywords = "Conformal structure, Density tensor, Invariant operator, Transvector",
author = "Sofiane Bouarroudj",
year = "2009",
month = "2",
day = "1",
doi = "10.1007/s11232-009-0012-8",
language = "English (US)",
volume = "158",
pages = "137--150",
journal = "Theoretical and Mathematical Physics(Russian Federation)",
issn = "0040-5779",
publisher = "Springer New York",
number = "2",

}

TY - JOUR

T1 - Ternary invariant differential operators acting on spaces of weighted densities

AU - Bouarroudj, Sofiane

PY - 2009/2/1

Y1 - 2009/2/1

N2 - We classify ternary differential operators over n-dimensional manifolds. These operators act on the spaces of weighted densities and are invariant with respect to the Lie algebra of vector fields. For n = 1, some of these operators can be expressed in terms of the de Rham exterior differential, the Poisson bracket, the Grozman operator, and the Feigin-Fuchs antisymmetric operators; four of the operators are new up to dualizations and permutations. For n > 1, we list multidimensional conformal tranvectors, i.e., operators acting on the spaces of weighted densities and invariant with respect to o(p + 1, q + 1), where p + q = n. With the exception of the scalar operator, these conformally invariant operators are not invariant with respect to the whole Lie algebra of vector fields.

AB - We classify ternary differential operators over n-dimensional manifolds. These operators act on the spaces of weighted densities and are invariant with respect to the Lie algebra of vector fields. For n = 1, some of these operators can be expressed in terms of the de Rham exterior differential, the Poisson bracket, the Grozman operator, and the Feigin-Fuchs antisymmetric operators; four of the operators are new up to dualizations and permutations. For n > 1, we list multidimensional conformal tranvectors, i.e., operators acting on the spaces of weighted densities and invariant with respect to o(p + 1, q + 1), where p + q = n. With the exception of the scalar operator, these conformally invariant operators are not invariant with respect to the whole Lie algebra of vector fields.

KW - Conformal structure

KW - Density tensor

KW - Invariant operator

KW - Transvector

UR - http://www.scopus.com/inward/record.url?scp=62949181421&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62949181421&partnerID=8YFLogxK

U2 - 10.1007/s11232-009-0012-8

DO - 10.1007/s11232-009-0012-8

M3 - Article

AN - SCOPUS:62949181421

VL - 158

SP - 137

EP - 150

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

IS - 2

ER -