论文标题
一类分级的保形代数，由海森伯格 - 维拉索罗共形代数诱导
A class of graded conformal algebras which is induced by Heisenberg-Virasoro conformal algebra
论文作者
论文摘要
在本文中，我们获得了$ \ mathbb {z} $的类别的分级保形代数，该代数由Heisenberg-virasoro保形代数诱导。更准确地说，我们对$ \ mathbb {z} $ - 分级保形代数$ \ mathcal {a} = \ oplus^\ infty_ {i = -1} \ Mathcal {a} _i $满足以下条件， （C1）$ \ MATHCAL {a} _0 $是Heisenberg-Virasoro Condomatal代数； C2）每个$ \ Mathcal {a} _i $ for $ i \ in \ Mathbb {z} _ {\ ge-1}^*$是$ \ Mathcal {a} _0 $ -Module，等级。 （c3）$ [{x _ { - 1}}_λx_i] \ neq 0 $ for $ i \ ge 0 $，其中$ x_i $是$ \ mathbb {c} [\ partial] $的任何一种，$ \ \ \ \ m nathcal {a} a} _i $ for $ i \ ge} 此外，我们证明，在某些特殊条件下，这些代数的所有有限的非平凡不可约模块都不是$ \ mathbb {c} [\ partial] $ - 模块。还确定了这类分级谎言共形代数的共形衍生物。
In this paper, we obtain a class of $\mathbb{Z}$-graded conformal algebras which is induced by Heisenberg-Virasoro conformal algebra. More precisely, we classify $\mathbb{Z}$-graded conformal algebras $\mathcal{A} = \oplus^\infty_{i=-1}\mathcal{A}_i$ satisfying the following conditions, (C1) $\mathcal{A}_0$ is the Heisenberg-Virasoro conformal algebra; C2) Each $\mathcal{A}_i$ for $i\in\mathbb{Z}_{\ge-1}^*$ is an $\mathcal{A}_0$-module of rank one; (C3) $[{X_{-1}}_λX_i]\neq 0$ for $i\ge 0$, where $X_i$ is any one of $\mathbb{C}[\partial]$-generators of $\mathcal{A}_i$ for $i\in \mathbb{Z}_{\ge -1}$. Further, we prove that all finite nontrivial irreducible modules of these algebras under some special conditions are free of rank one as a $\mathbb{C}[\partial]$-module. The conformal derivations of this class of graded Lie conformal algebras are also determined.
