论文标题
Heisenberg顶点操作员代数的第二级Zhu代数
The level two Zhu algebra for the Heisenberg vertex operator algebra
论文作者
论文摘要
我们确定了Heisenberg顶点操作员代数$ V $的第二个Zhu代数，用于任何选择的共形元素。我们仅使用$ v $：$ v $的内部结构的以下信息来执行此操作；第二作者已经确定的$ v $的一级朱代数以及范德·沃夫（Vander Werf）和杨（Yang）；以及较低级的Zhu代数提供的有关不可还原模块的信息。通过采用一般结果和技术来确定高级Zhu eargebras和barron，Aldbbo和Barron，我们能够使用最小的信息来对$ v $进行$ v $的第二级Zhu代数的计算。特别是，我们表明，海森伯格顶点操作员代数为$ n $ n $ zhu代数为$ n = 2 $的级别。我们还为Heisenberg Vertex操作员代数代数为$ n $ Zhu代数的结构做出了猜想，任何$ n> 2 $。
We determine the level two Zhu algebra for the Heisenberg vertex operator algebra $V$ for any choice of conformal element. We do this using only the following information for $V$: the internal structure of $V$; the level one Zhu algebra of $V$ already determined by the second author, along with Vander Werf and Yang; and the information the lower level Zhu algebras give regarding irreducible modules. We are able to carry out this calculation of the level two Zhu algebra for $V$ with this minimal information by employing the general results and techniques for determining generators and relations for higher level Zhu algebras for a vertex operator algebra, as developed previously by the authors in "On generators and relations for higher level Zhu algebras and applications", by Addabbo and Barron, J. Algebra, 2023. In particular, we show that the level $n$ Zhu algebras for the Heisenberg vertex operator algebra become noncommutative at level $n=2$. We also give a conjecture for the structure of the level $n$ Zhu algebra for the Heisenberg vertex operator algebra, for any $n >2$.
