2008/12/17 by Li, Haisheng
#17B68 #17B69 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.0812.3156
This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we study notions of ℏ-adic nonlocal vertex algebra and ℏ-adic (weak) quantum vertex algebra, slightly generalizing Etingof-Kazhdan's notion of quantum vertex operator algebra. For any topologically free \C[[\h]]-module W, we study ℏ-adically compatible subsets and ℏ-adically §-local subsets of (\End W)[[x,x-1]]. We prove that any ℏ-adically compatible subset generates an ℏ-adic nonlocal vertex algebra with W as a module and that any ℏ-adically §-local subset generates an ℏ-adic weak quantum vertex algebra with W as a module. A general construction theorem of ℏ-adic nonlocal vertex algebras and ℏ-adic quantum vertex algebras is obtained. As an application we associate the centrally extended double Yangian of \sl2 to ℏ-adic quantum vertex algebras.