论文标题
$ n $ -lie保形代数及其相关的无限维$ n $ -lie代数
$n$-Lie conformal algebras and its associated infinite-dimensional $n$-Lie algebras
论文作者
论文摘要
在本文中，我们将$ \ {λ_{1 \ to to n-1} \} $ - 括号和$ n $ -lie保串代数的分布概念。对于任何$ n $ -lie综合代数$ r $，都存在一系列相关的无限维线性紧凑$ n $ -n $ -lie algebras $ \ {（\ Mathscr {l} ie_p \ mbox \ mbox {} r）我们表明，当且仅当$（\ Mathscr {\ Mathscr {l} ie_p \ mbox {} r）_ \ _ \ _ \ _ \ simeq（\ simeq（\ Mathscr {l} ie__p \ mbox \ mbox \ aboberem）时$ n $ -lie代数带有$ \ partial_ {t_i} $ - 任何$ p \ ge1 $的操作。此外，建立了$ n $ -lie保串代数的代表性和协同学理论。特别是，$ r $的复合物是$ n $ -lie代数$（\ Mathscr {l} ie_p \ mbox {} r）_ \ _ $的子复合物。
In this paper, we introduce a $\{λ_{1\to n-1}\}$-bracket and a distribution notion of an $n$-Lie conformal algebra. For any $n$-Lie conformal algebra $R$, there exists a series of associated infinite-dimensional linearly compact $n$-Lie algebras $\{(\mathscr{L}ie_p\mbox{ }R)_\_\}_{(p\ge1)}$. We show that torsionless finite $n$-Lie conformal algebras $R$ and $S$ are isomorphic if and only if $(\mathscr{L}ie_p\mbox{ }R)_\_\simeq (\mathscr{L}ie_p\mbox{ }S)_\_$ as linearly compact $n$-Lie algebras with $\partial_{t_i}$-action for any $p\ge1$. Moreover, the representation and cohomology theory of $n$-Lie conformal algebras are established. In particular, the complex of $R$ is isomorphic to a subcomplex of $n$-Lie algebra $(\mathscr{L}ie_p\mbox{ }R)_\_$.
