منابع مشابه
Quasi-derivations and quasi-algebroids
Axioms of Lie algebroid are discussed. In particular, it is shown that a Lie quasi-algebroid (i.e. a Lie algebra bracket on the C∞(M)-module E of sections of a vector bundle E over a manifold M which satisfies [X, fY ] = f [X, Y ] + A(X,f)Y for all X, Y ∈ E , f ∈ C∞(M), and for certain A(X,f) ∈ C∞(M)) is a Lie algebroid if rank(E) > 1, and is a local Lie algebra in the sense of Kirillov if E is...
متن کاملQuasi-derivations and QD-algebroids
Axioms of Lie algebroid are discussed. In particular, it is shown that a Lie QD-algebroid (i.e. a Lie algebra bracket on the C∞(M)-module E of sections of a vector bundle E over a manifold M which satisfies [X, fY ] = f [X, Y ] + A(X,f)Y for all X, Y ∈ E , f ∈ C∞(M), and for certain A(X,f) ∈ C∞(M)) is a Lie algebroid if rank(E) > 1, and is a local Lie algebra in the sense of Kirillov if E is a ...
متن کاملA New Look at the Schouten-Nijenhuis, Frölicher-Nijenhuis and Nijenhuis-Richardson Brackets for Symplectic Spaces
In this paper we re-express the Schouten-Nijenhuis, the Frölicher-Nijenhuis and the Nijenhuis-Richardson brackets on a symplectic space using the extended Poisson brackets structure present in the path-integral formulation of classical mechanics.
متن کاملZeros of Quasi-Orthogonal Jacobi Polynomials
We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by α > −1, −2 < β < −1. We give necessary and sufficient conditions under which a conjecture by Askey, that the zeros of Jacobi polynomials P (α,β) n and P (α,β+2) n are interlacing, holds when the parameters α and β are in the range α > −1 and −2 < β < −1. We prove that t...
متن کاملNijenhuis Integrability for Killing Tensors
The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton–Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis integrability conditions. The latter are a system of three non-linear partial differential equations. We give a simple and completely algebraic proof that for...
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ژورنال
عنوان ژورنال: Reports on Mathematical Physics
سال: 2010
ISSN: 0034-4877
DOI: 10.1016/s0034-4877(10)80021-7