6533b7d0fe1ef96bd125adb6
RESEARCH PRODUCT
On the Leibniz bracket, the Schouten bracket and the Laplacian
Joan Josep FerrandoBartolomé Collsubject
PhysicsPure mathematicsCommutatorMathematics::History and OverviewMathematics::Rings and AlgebrasStructure (category theory)FOS: Physical sciencesStatistical and Nonlinear PhysicsGeneral Relativity and Quantum Cosmology (gr-qc)General Relativity and Quantum CosmologyOperator (computer programming)Bracket (mathematics)Nonlinear Sciences::Exactly Solvable and Integrable SystemsProduct (mathematics)Mathematics::Quantum AlgebraLie algebra[PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph]Laplace operatorExterior algebraMathematics::Symplectic GeometryMathematical Physicsdescription
International audience; The Leibniz bracket of an operator on a (graded) algebra is defined and some of its properties are studied. A basic theorem relating the Leibniz bracket of the commutator of two operators to the Leibniz bracket of them is obtained. Under some natural conditions, the Leibniz bracket gives rise to a (graded) Lie algebra structure. In particular, those algebras generated by the Leibniz bracket of the divergence and the Laplacian operators on the exterior algebra are considered, and the expression of the Laplacian for the product of two functions is generalized for arbitrary exterior forms.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-06-22 |