Lie brackets

Xem 1-5 trên 5 kết quả Lie brackets
  • In this paper we present the solution to a longstanding problem of differential geometry: Lie’s third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we derive, explain and improve the known integrability results, we establish integrability by local Lie groupoids, we clarify the smoothness of the Poisson sigma-model for Poisson manifolds, and we describe other geometrical applications. Contents 0. Introduction

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  • We identify the symmetry algebra of the Laplacian on Euclidean space as an explicit quotient of the universal enveloping algebra of the Lie algebra of conformal motions. We construct analogues of these symmetries on a general conformal manifold. 1. Introduction The space of smooth first order linear differential operators on Rn that preserve harmonic functions is closed under Lie bracket. For n ≥ 3, it is finitedimensional (of dimension (n2 + 3n + 4)/2). Its commutator subalgebra is isomorphic to so(n + 1, 1), the Lie algebra of conformal motions of Rn .

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  • Maximum allowed number of bisections. float rtbis(float (*func)(float), float x1, float x2, float xacc) Using bisection, find the root of a function func known to lie between x1 and x2. The root, returned as rtbis, will be refined until its accuracy is ±xacc. { void nrerror(char error_text[]); int j; float dx,f,fmid,xmid,rtb; f=(*func)(x1); fmid=(*func)(x2); if (f*fmid = 0.0) nrerror("Root must be bracketed for bisection in rtbis"); rtb = f 0 for (j=1;j

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  • 231 Force: The complementisers that/if in a sentence such as I didn’t know [that/if he was lying] are said to indicate that the bracketed clauses are declarative/interrogative in force (in the sense that they have the force of a question/a statement). In work on split CP projections by Luigi Rizzi (discussed in §9.2-§9.3), complementisers are said to constitute a Force head which can project into a Force Phrase.

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  • Dedicated to Yum-Tong Siu for his 60th birthday. Abstract Let {X1 , . . . , Xp } be complex-valued vector fields in Rn and assume that they satisfy the bracket condition (i.e. that their Lie algebra spans all vector fields). Our object is to study the operator E = Xi∗ Xi , where Xi∗ is the L2 adjoint of Xi . A result of H¨rmander is that when the Xi are real then E is o hypoelliptic and furthemore it is subelliptic (the restriction of a destribution u to an open set U is “smoother” then the restriction...

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