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Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
The Carroll group was originally introduced by Levy-Leblond (1965 Ann. Inst. Henri Poincare 3 1) by considering the contraction of the Poincare group as c → 0. In this paper an alternativeExpand
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The exotic Galilei group and the “Peierls substitution”
Taking advantage of the two-parameter central extension of the planar Galilei group, we construct a non relativistic particle model in the plane. Owing to the extra structure, the coordinates do notExpand
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Non-relativistic conformal symmetries and Newton–Cartan structures
This paper provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton–Cartan spacetime. The Lie algebras of non-relativistic conformalExpand
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Conformal Carroll groups and BMS symmetry
The Bondi–Metzner–Sachs group is shown to be the conformal extension of Levy-Leblond's 'Carroll' group. Further extension to the Newman–Unti group is also discussed in the Carroll framework.
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Conformally equivariant quantization: existence and uniqueness
On etablit l'existence et l'unicite d'un calcul symbolique et d'une quantification conformement equivariants sur une variete pseudo-riemannienne conformement plate (M, g), i.e. on met en evidence unExpand
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Space of second order linear differential operators as a module over the Lie algebra of vector fields
Abstract The space of linear differential operators on a smooth manifoldMhas a natural one-parameter family of Diff(M)- (and Vect(M)-) module structures, defined by their action on the space ofExpand
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Pukanszky's condition and symplectic induction
Pukanszky’s condition is a condition used in obtaining representations from coadjoint orbits. In order to obtain more geometric insight in this condition, we relate it to symplectic induction. ItExpand
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Conformally equivariant quantization
Let $(M,g)$ be a pseudo-Riemannian manifold and $F_\lambda(M)$ the space of densities of degree $\lambda$ on $M$. We study the space $D^2_{\lambda,\mu}(M)$ of second-order differential operators fromExpand
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Conformal Carroll groups
Conformal extensions of Levy–Leblondʼs Carroll group, based on geometric properties analogous to those of Newton–Cartan space-time are proposed. The extensions are labeled by an integer k. ThisExpand
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Exotic Galilean symmetry in the non-commutative plane and the Hall effect
Quantum mechanics in the non-commutative plane is shown to admit the 'exotic' symmetry of the doubly centrally extended Galilei group. When coupled to a planar magnetic field whose strength is theExpand
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