# Galilean conformal algebras in two spatial dimension

@article{Aizawa2011GalileanCA, title={Galilean conformal algebras in two spatial dimension}, author={Naruhiko Aizawa and Yuta Kimura}, journal={arXiv: Mathematical Physics}, year={2011} }

A class of infinite dimensional Galilean conformal algebra in (2+1) dimensional spacetime is studied. Each member of the class, denoted by \alg_{\ell}, is labelled by the parameter \ell. The parameter \ell takes a spin value, i.e., 1/2, 1, 3/2, .... We give a classification of all possible central extensions of \alg_{\ell}. Then we consider the highest weight Verma modules over \alg_{\ell} with the central extensions. For integer \ell we give an explicit formula of Kac determinant. It results…

## 13 Citations

### Some representations of planar Galilean conformal algebra

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Representation theory of an infinite dimensional Galilean conformal algebra introduced by Martelli and Tachikawa is developed. We focus on the algebra defined in (2 + 1) dimensional spacetime and…

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An explicit canonical realization of the conformal extension of BMS_{3} is shown to emerge from the asymptotic structure of conformal gravity in three dimensions, endowed with a new set of boundary conditions.

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We study some generic aspects of CFTs with the BMS${}_3$ algebra defined as a chiral symmetry. These theories are realized through the isomorphism between the BMS${}_3$ and the $W(2,2)$ algebras. For…

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The analysis previously developed in [J. Math. Phys. 55 102901 (2014)] is used to construct systems which hold invariant under N=2l-conformal Galilei superalgebra. The models describe two different…

### N=2 supersymmetric extension of l-conformal Galilei algebra

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N=2 supersymmetric extension of the l-conformal Galilei algebra is constructed. A relation between its representations in flat spacetime and in Newton-Hooke spacetime is discussed. An…

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- MathematicsQuaestiones Mathematicae
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Abstract In this paper, the biderivations of the Galiean conformal algebra are determined. As an application, the forms of the commutative post-Lie algebra structures on the Galiean conformal algebra…

### NONRELATIVISTIC HOLOGRAPHY — A GROUP-THEORETICAL PERSPECTIVE

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We give a review of some group-theoretical results related to nonrelativistic holography. Our main playgrounds are the Schrodinger equation and the Schrodinger algebra. We first recall the…

### The (super)conformal BMS$_3$ algebra

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Oscar Fuentealba,a Hernán A. González,b Alfredo Pérez,c David Tempod and Ricardo Troncoso.c Université Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine CP231, B-1050…

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Representation theory of an infinite dimensional Galilean conformal algebra introduced by Martelli and Tachikawa is developed. We focus on the algebra defined in (2 + 1) dimensional spacetime and…

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