量子仿射顶点代数的过滤与分次
Filtration and gradation of quantum affine vertex algebras
AI总结：
该文对与双杨代数等相关的量子仿射顶点代数进行统一构造，展示其含带递增过滤的稠密量子顶点子代数，且证明相关分次代数同构于特定的\(\mathbb Z\)-分次稠密量子顶点子代数。
AI中文摘要：
本文给出了与双杨代数、非扭量子仿射化代数和扭量子仿射化代数相关的量子仿射顶点代数的统一构造。证明了这些\(\hbar\)-adic量子顶点代数包含一个配备递增过滤的稠密量子顶点子代数。还证明了关于这些过滤的相关分次代数同构于与双杨代数相关的量子仿射顶点代数的\(\mathbb Z\)-分次稠密量子顶点子代数。
英文摘要：
In this paper, we present a unified construction of quantum affine vertex algebras associated to double Yangians, untwisted quantum affinization algebras, and twisted quantum affinization algebras. We show that these $\hbar$-adic quantum vertex algebras contain a dense quantum vertex subalgebra equipped with a increasing filtration. Moreover, we prove that the associated graded algebras with respect to these filtrations are isomorphic to a $\mathbb Z$-graded dense quantum vertex subalgebra of the quantum affine vertex algebras associated to double Yangians.
