Abstract
Galilean conformal algebras can be constructed by contracting a finite number of conformal algebras, and enjoy truncated Z-graded structures. Here, we present a generalisation of the Galilean contraction procedure, giving rise to Galilean conformal algebras with truncated Z⊗σ-gradings, σ∈N. Detailed examples of these multi-graded Galilean algebras are provided, including extensions of the Galilean Virasoro and affine Kac-Moody algebras. We also derive the associated Sugawara constructions and discuss how these examples relate to multivariable extensions of Takiff algebras. We likewise apply our generalised contraction prescription to tensor products of W3 algebras and obtain new families of higher-order Galilean W3 algebras.
Highlights
The Galilean Virasoro algebra appears in studies of asymptotically flat three-dimensional spacetimes, see [1] and references therein, and can be constructed [2,3,4,5,6] as a contraction of a pair of Virasoro algebras
The Galilean W3 algebra [7,8,9,10,11] follows by contracting a pair of W3 algebras, while more general Galilean conformal algebras with extended symmetries have been constructed in [9,11,12] and are known as Galilean W -algebras
In the case of Virasoro or affine KacMoody, the usual second-order Galilean algebras have been found [20] to be isomorphic to the Takiff algebras [21] considered in [22, 23], while the higher-order counterparts provide N th-order generalisations
Summary
The Galilean Virasoro algebra appears in studies of asymptotically flat three-dimensional spacetimes, see [1] and references therein, and can be constructed [2,3,4,5,6] as a contraction of a pair of Virasoro algebras. In the case of Virasoro or affine KacMoody, the usual second-order Galilean algebras have been found [20] to be isomorphic to the Takiff algebras [21] considered in [22, 23], while the higher-order counterparts provide N th-order generalisations (where N is the number of inputted symmetry algebras A). These higher-order Galilean algebras enjoy a truncated Z-grading whose truncation is determined by the order N of the contraction
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