论文标题
多级伽利利亚形成代数
Multi-graded Galilean conformal algebras
论文作者
论文摘要
可以通过签约有限数量的保形代数，并享受截断的$ \ mathbb {z} $ - 分级结构来构建galilean共形代数。在这里，我们介绍了加利利收缩程序的概括，从而引起了galilean conformal代数，并带有截短的$ \ mathbb {z}^{\otimesσ} $ - 级别，$σ\ in \ in \ mathbb {n} $。提供了这些多级伽利略代数的详细示例，包括加利亚·维拉索罗的扩展和offine kac-moody代数。我们还得出了相关的Sugawara构造，并讨论了这些示例如何与Tabiff代数的多变量扩展有关。同样，我们将广义收缩处方应用于$ W_3 $代数的张量产品，并获得高阶Galilean $ W_3 $代数的新家族。
Galilean conformal algebras can be constructed by contracting a finite number of conformal algebras, and enjoy truncated $\mathbb{Z}$-graded structures. Here, we present a generalisation of the Galilean contraction procedure, giving rise to Galilean conformal algebras with truncated $\mathbb{Z}^{\otimesσ}$-gradings, $σ\in\mathbb{N}$. 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 $W_3$ algebras and obtain new families of higher-order Galilean $W_3$ algebras.
