Arc spaces and the vertex algebra commutant problem
Arc spaces and the vertex algebra commutant problem
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弧空间与顶点代数交换问题
DOI：
10.1016/j.aim.2015.03.007
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Bailin Song
中科院分区：
文献类型：
--
作者：
A. Linshaw;Gerald W. Schwarz;Bailin Song
给定一个顶点代数V和子代数A⊂V，交换子Com(A，V)是V的与A的所有元素交换的子代数。这种构造类似于结合代数理论中的普通交换子，在构造陪集共形场论中具有重要的物理意义。当A是仿射顶点代数时，Com(A，V)与弧空间上的不变函数环密切相关。我们找到了一族例子的强有限生成集，其中A是仿射的，V是βγ系、bc系或bcβγ系。
Given a vertex algebra V and a subalgebra A⊂ V, the commutant Com (A, V) is the subalgebra of V which commutes with all elements of A. This construction is analogous to the ordinary commutant in the theory of associative algebras, and is important in physics in the construction of coset conformal field theories. When A is an affine vertex algebra, Com (A, V) is closely related to rings of invariant functions on arc spaces. We find strong finite generating sets for a family of examples where A is affine and V is a βγ-system, bc-system, or b c β γ-system.