Modules-at-infinity for quantum vertex algebras

Details Modules-at-infinity for quantum vertex algebras Modules-at-infinity for quantum vertex algebras

2007-05-04

arxiv.org/abs/0705.0687v1

Mathematics

Quantum Algebra

Latex, 48 pages

Scientific paper

10.1007/s00220-008-0534-1

This is a sequel to \cite{li-qva1} and \cite{li-qva2} in a series to study vertex algebra-like structures arising from various algebras such as quantum affine algebras and Yangians. In this paper, we study two versions of the double Yangian $DY_{\hbar}(sl_{2})$, denoted by $DY_{q}(sl_{2})$ and $DY_{q}^{\infty}(sl_{2})$ with $q$ a nonzero complex number. For each nonzero complex number $q$, we construct a quantum vertex algebra $V_{q}$ and prove that every $DY_{q}(sl_{2})$-module is naturally a $V_{q}$-module. We also show that $DY_{q}^{\infty}(sl_{2})$-modules are what we call $V_{q}$-modules-at-infinity. To achieve this goal, we study what we call $\S$-local subsets and quasi-local subsets of $\Hom (W,W((x^{-1})))$ for any vector space $W$, and we prove that any $\S$-local subset generates a (weak) quantum vertex algebra and that any quasi-local subset generates a vertex algebra with $W$ as a (left) quasi module-at-infinity. Using this result we associate the Lie algebra of pseudo-differential operators on the circle with vertex algebras in terms of quasi modules-at-infinity.

Affiliated with

Also associated with

No associations

Rating

Modules-at-infinity for quantum vertex algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Modules-at-infinity for quantum vertex algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modules-at-infinity for quantum vertex algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-616391