论文标题
顶点代数的最简单的同胞不变性
The simplest cohomological invariants for vertex algebras
论文作者
论文摘要
对于在\ cite {huang}中定义的分级限制性顶点代数共同体的双重复杂结构，我们引入了双复杂空间的元素的乘法。我们表明，在双重复杂空间上应用的正交性和双重分级条件在映射和联合运营商的作用之间提供了相关性。因此，我们将双重复合空间赋予双级差分代数的结构。然后，我们为限制性顶点代数介绍了Simples共同体学类，并展示了它们独立于从双重复杂空间中选择映射的独立性。我们证明其同胞类别不取决于代表双重复杂空间的映射。最后，我们表明，正交关系以及双重分级条件带来了持续谎言代数的发电机和换向关系。
For the double complex structure of grading-restricted vertex algebra cohomology defined in \cite{Huang}, we introduce a multiplication of elements of double complex spaces. We show that the orthogonality and bi-grading conditions applied on double complex spaces, provide in relation among mappings and actions of co-boundary operators. Thus, we endow the double complex spaces with structure of bi-graded differential algebra. We then introduce the simples cohomology classes for a grading-restricted vertex algebra, and show their independence on the choice of mappings from double complex spaces. We prove that its cohomology class does not depend on mappings representing of the double complex spaces. Finally, we show that the orthogonality relations together with the bi-grading condition bring about generators and commutation relations for a continual Lie algebra.
