- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- $q$-Virasoro algebra and affine Lie algebras
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
$q$-Virasoro algebra and affine Lie algebras Li, Haisheng
Description
In this talk, I will discuss a natural connection of a certain $q$-Virasoro algebra with affine Lie algebras and vertex algebras. To any abelian group $S$ with a linear character, we associate an infinite-dimensional Lie algebra $D_{S}$. When $S=\Z$ with $\chi$ defined by $\chi(n)=q^{n}$ with $q$ a nonzero complex number, $D_{S}$ reduces to the $q$-Virasoro algebra $D_{q}$ which was introduced in \cite{BC}. We also introduce a Lie algebra $\g_{S}$ with $S$ as an automorphism group and we prove that $D_{S}$ is isomorphic to the $S$-covariant algebra of the affine Lie algebra $\widehat{\g_{S}}$. Then we relate restricted $D_{S}$-modules of level $\ell\in \C$ with equivariant quasi modules for the vertex algebra $V_{\widehat{\g_{S}}}(\ell,0)$. Furthermore, we show that if $S$ is a finite abelian group of order $2l+1$, $D_{S}$ is isomorphic to the affine Kac-Moody algebra of type $B^{(1)}_{l}$. This talk is based on a joint work with Hongyan Guo, Shaobin Tan and Qing Wang.
Item Metadata
Title |
$q$-Virasoro algebra and affine Lie algebras
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2016-02-10T11:30
|
Description |
In this talk, I will discuss a natural connection of a certain
$q$-Virasoro algebra with affine Lie algebras and vertex algebras.
To any abelian group $S$ with a linear character, we associate an
infinite-dimensional Lie algebra $D_{S}$.
When $S=\Z$ with $\chi$ defined by $\chi(n)=q^{n}$ with $q$ a nonzero
complex number, $D_{S}$ reduces to the $q$-Virasoro algebra $D_{q}$
which was introduced in \cite{BC}. We also introduce a Lie algebra
$\g_{S}$ with $S$ as an automorphism group and
we prove that $D_{S}$ is isomorphic to the $S$-covariant algebra of the
affine Lie algebra $\widehat{\g_{S}}$.
Then we relate restricted $D_{S}$-modules of level $\ell\in \C$ with
equivariant quasi modules
for the vertex algebra $V_{\widehat{\g_{S}}}(\ell,0)$.
Furthermore, we show that if $S$ is a finite abelian group of order
$2l+1$, $D_{S}$ is
isomorphic to the affine Kac-Moody algebra of type $B^{(1)}_{l}$.
This talk is based on a joint work with Hongyan Guo, Shaobin Tan and
Qing Wang.
|
Extent |
44 minutes
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: Rutgers University at Camden
|
Series | |
Date Available |
2016-08-11
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0307472
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Faculty
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International