论文标题
$ n = 2 $ lie Condormal Superalgebras的有限不可约包模块的分类
Classification of finite irreducible conformal modules over $N=2$ Lie conformal superalgebras of Block type
论文作者
论文摘要
我们介绍了$ n = 2 $ lie Superalgebras $ {\ frak {k}}（p）block类型的$，并将其有限的不可减至的共形模块分类为任何非零参数$ p $。其中$ p $是一个非零的复数数字。特别是，我们表明，这样的保形模块承认有限的共形模块$ m $ $ m $超过$ k_2 $，如果$ p = -1 $和$ m $具有排名$（2+2）$，其中$ k_2 $是$ n = 2 $ conformal subalgebra of $ $ {\ frak of $ {\ frak {\ frak {\ frak {\ k {作为副产品，我们在一系列有限的谎言中，将有限的不可约合形模块分类用于$ n \ ge1 $的一系列有限的谎言condormal superalgebras $ {\ frak k}（n）$。还确定了所有涉及的还原共形模块的组成因子。
We introduce the $N=2$ Lie conformal superalgebras ${\frak {K}}(p)$ of Block type, and classify their finite irreducible conformal modules for any nonzero parameter $p$. where $p$ is a nonzero complex number. In particular, we show that such a conformal module admits a nontrivial extension of a finite conformal module $M$ over $K_2$ if $p=-1$ and $M$ has rank $(2+2)$, where $K_2$ is an $N=2$ conformal subalgebra of ${\frak {K}}(p)$. As a byproduct, we obtain the classification of finite irreducible conformal modules over a series of finite Lie conformal superalgebras ${\frak k}(n)$ for $n\ge1$. Composition factors of all the involved reducible conformal modules are also determined.
