## Abstract

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 h{stroke}-adic nonlocal vertex algebra and h{stroke}-adic (weak) quantum vertex algebra, slightly generalizing Etingof-Kazhdan's notion of quantum vertex operator algebra. For any topologically free c[[h{stroke}]]-module W, we study h{stroke}-adically compatible subsets and h{stroke}-adically S-local subsets of (End W)[[x, x^{-1}]]. We prove that any h{stroke}-adically compatible subset generates an h{stroke}-adic nonlocal vertex algebra with W as a module and that any h{stroke}-adically S-local subset generates an h{stroke}-adic weak quantum vertex algebra with W as a module. A general construction theorem of h{stroke}-adic nonlocal vertex algebras and h{stroke}-adic quantum vertex algebras is obtained. As an application we associate the centrally extended double Yangian of sl_{2} to h{stroke}-adic quantum vertex algebras.

Original language | English (US) |
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Pages (from-to) | 475-523 |

Number of pages | 49 |

Journal | Communications In Mathematical Physics |

Volume | 296 |

Issue number | 2 |

DOIs | |

State | Published - 2010 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics